The perfectly matched layer is an absorbing boundary layer used in modelling wave propagation in unbounded media to prevent spurious wave reflections from the end faces of the computational domain. However, numerical discretisation can cause wave reflections from the perfectly matched layer. We validate the implementation of the perfectly matched layer in finite element modelling by comparing the numerical results with an analytical solution. Computed wave reflections range from 6.5% to 32% of the maximum theoretical displacement. Decreasing the Courant-Friedrichs-Lewy number can reduce reflections from the perfectly matched layer.