diff --git a/NEWS.md b/NEWS.md
index bf5c176d8..db59c20ef 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -11,7 +11,7 @@
 - The interface for defining delay distributions has been generalised to also cater for continuous distributions
 - When defining probability distributions these can now be truncated using the `tolerance` argument
 - Ornstein-Uhlenbeck and 5 / 2 Matérn kernels have been added. By @sbfnk in #741 and reviewed by @seabbs.
-- Gaussian processes have been vectorised and the `gp_opts()` function has been updated to allow for the specification of a periodic kernel. By @seabbs in #742 and reviewed by @jamesmbaazam.
+- Gaussian processes have been vectorised and the `gp_opts()` function has been updated to allow for the specification of periodic and linear kernels. By @seabbs in #742 and reviewed by @jamesmbaazam.
 - Prior predictive checks have been used to update the following priors: the prior on the magnitude of the Gaussian process (from HalfNormal(0, 1) to HalfNormal(0, 0.1)), and the prior on the overdispersion (from 1 / HalfNormal(0, 1)^2 to 1 / HalfNormal(0, 0.25)). By @seabbs in #742 and reviewed by @jamesmbaazam.
 - The default stan control options have been updated from `list(adapt_delta = 0.95, max_treedepth = 15)` to `list(adapt_delta = 0.9, max_treedepth = 12)` due to improved performance and to reduce the runtime of the default parameterisations. By @seabbs in #742 and reviewed by @jamesmbaazam.
 - Initialisation has been simplified by sampling directly from the priors, where possible, rather than from a constrained space. By @seabbs in #742 and reviewed by @jamesmbaazam.
diff --git a/man/gp_opts.Rd b/man/gp_opts.Rd
index c9fa19063..1a3882c1c 100644
--- a/man/gp_opts.Rd
+++ b/man/gp_opts.Rd
@@ -13,7 +13,7 @@ gp_opts(
   ls_max = 60,
   alpha_mean = 0,
   alpha_sd = 0.01,
-  kernel = c("matern", "se", "ou", "periodic"),
+  kernel = c("matern", "se", "ou", "periodic", "linear"),
   matern_order = 3/2,
   matern_type,
   w0 = 1
@@ -32,18 +32,19 @@ approximate Gaussian process. See (Riutort-Mayol et al. 2020
 \url{https://arxiv.org/abs/2004.11408}) for advice on updating this default.}
 
 \item{ls_mean}{Numeric, defaults to 21 days. The mean of the lognormal
-length scale.}
+length scale. Not used for linear kernel.}
 
 \item{ls_sd}{Numeric, defaults to 7 days. The standard deviation of the log
 normal length scale. If \code{ls_sd = 0}, inverse-gamma prior on Gaussian
 process length scale will be used with recommended parameters
-\code{inv_gamma(1.499007, 0.057277 * ls_max)}.}
+\code{inv_gamma(1.499007, 0.057277 * ls_max)}. Not used for linear kernel.}
 
-\item{ls_min}{Numeric, defaults to 0. The minimum value of the length scale.}
+\item{ls_min}{Numeric, defaults to 0. The minimum value of the length scale.
+Not used for linear kernel.}
 
 \item{ls_max}{Numeric, defaults to 60. The maximum value of the length
 scale. Updated in \code{\link[=create_gp_data]{create_gp_data()}} to be the length of the input data if
-this is smaller.}
+this is smaller. Not used for linear kernel.}
 
 \item{alpha_mean}{Numeric, defaults to 0. The mean of the magnitude parameter
 of the Gaussian process kernel. Should be approximately the expected variance
@@ -55,7 +56,8 @@ the expected standard deviation of the logged Rt.}
 
 \item{kernel}{Character string, the type of kernel required. Currently
 supporting the squared exponential kernel ("se"), periodic kernel
-("periodic"), Ornstein-Uhlenbeck kernel ("ou"), and Matern kernel ("matern").}
+("periodic"), Ornstein-Uhlenbeck kernel ("ou"), Matern kernel ("matern"),
+and linear kernel ("linear").}
 
 \item{matern_order}{Numeric, defaults to 3/2. Order of Matérn Kernel to use.
 Common choices are 1/2, 3/2, and 5/2. If \code{kernel} is set
@@ -82,4 +84,7 @@ gp_opts()
 
 # add a custom length scale
 gp_opts(ls_mean = 4)
+
+# use linear kernel
+gp_opts(kernel = "linear")
 }
diff --git a/tests/testthat/test-create_gp_data.R b/tests/testthat/test-create_gp_data.R
index d97b38824..2338e9cb3 100644
--- a/tests/testthat/test-create_gp_data.R
+++ b/tests/testthat/test-create_gp_data.R
@@ -54,7 +54,5 @@ test_that("create_gp_data correctly handles linear kernel", {
   data <- list(t = 30, seeding_time = 7, horizon = 7, future_fixed = 0, fixed_from = 0, stationary = 0)
   linear_gp_opts <- gp_opts(kernel = "linear")
   gp_data <- create_gp_data(linear_gp_opts, data)
-  
-  # Check that gp_type is set to 3 for linear kernel
   expect_equal(gp_data$gp_type, 3)
 })
\ No newline at end of file