We investigate the accuracy in the recovery of the stellar dynamics of barred galaxies when using axisymmetric dynamical models. We do this by trying to recover the mass-to-light ratio (M/L) and the anisotropy of realistic galaxy simulations using the Jeans Anisotropic Multi-Gaussian Expansion (JAM) modelling method. However, given that the biases we find are mostly due to an application of an axisymmetric modelling algorithm to a non-axisymmetric system and in particular to inaccuracies in the deprojected mass model, our results are relevant for general axisymmetric modelling methods. We run N-body collisionless simulations to build a library with various luminosity distribution, constructed to mimic real individual galaxies, with realistic anisotropy. The final result of our evolved library of simulations contains both barred and unbarred galaxies. The JAM method assumes an axisymmetric mass distribution, and we adopt a spatially constant M/L and anisotropy distributions. The models are fitted to two-dimensional maps of the second velocity moments of the simulations for various viewing angles [position angle (PA) of the bar and inclination of the galaxy]. We find that the inclination is generally well recovered by the JAM models, for both barred and unbarred simulations. For unbarred simulations the M/L is also accurately recovered, with negligible median bias and with a maximum one of just Δ(M/L) < 1.5 per cent when the galaxy is not too close to face on. At very low inclinations the M/L can be significantly overestimated (9 per cent in our tests, but errors can be larger for very face-on views). This is in agreement with previous studies. For barred simulations the M/L is on average (when PA = 45°) essentially unbiased, but we measure an over/underestimation of up to Δ(M/L) = 15 per cent in our tests. The sign of the M/L bias depends on the PA of the bar as expected: overestimation occurs when the bar is closer to end-on, due to the increased stellar motion along the line-of-sight, and underestimation otherwise. For unbarred simulations, the JAM models are able to recover the mean value of the anisotropy with bias, within the region constrained by the kinematics. However when a bar is present, or for nearly face-on models, the recovered anisotropy varies wildly, with biases up to Δβ z≈ 0.3.