The numerical implementation of the parabolised stability equations (PSE) using a spectral/ hp-element discretisation is considered, and the numerical stability of the governing equations is presented. Analogous to the primitive variable form of the two-dimensional PSE, the equations are ill-posed; although choosing an Euler implicit scheme in the streamwise z-direction yields a stable scheme for sufficiently large step sizes ( Δ z > 1 / | β | , where β is the streamwise wavenumber). The source of the instability is a residual ellipticity that remains in the equations, and presents itself as an upstream propagating acoustic wave. Neglecting this term relaxes the lower limit on the step-size restriction. The θ-scheme is also considered, allowing the step-size restriction of the scheme to be determined. The explicit scheme is always unstable, whereas neglecting the pressure gradient term shows stable eigenspectra for θ ⩾ 0.5 .