Numerical errors of PALLAS calculation due to special mesh size sare examined for a typical deep penetration shielding problem of isotropic incident fission neutrons penetrating a 200-cm-thick water slab. The exponential approximation for the source spatial distribution to solve the transport equation based on the direct integration method is verified to be effective for radition transport in attenuating medium, while the linear approximation employed in the old PALLAS code is found to produce large errors for calculations with large mesh sizes.