Steady state two-dimensional analytical solutions are derived for sediment velocity and rate of fluid expulsion in a thickening accretionary prism with smooth upper and lower surfaces. Two different kinematic assumptions lead to two similar sets of solutions. In one case, the sediment flow lines are assumed to diverge uniformly landward. In the other case, the horizontal velocity of any given sediment column is assumed uniform. By further assuming zero horizontal Darcy velocity in the prism, expressions can be obtained for the approximate vertical fluid velocity and pore fluid pressure fields. Results from applying these solutions to the Cascadia accretionary prism off Vancouver Island show the importance of modeling he effects of lateral as well as vertical porosity variation on the hydrogeology of the prism. These solutions provide a means to estimate fluid flow and pore pressure distribution for prisms with realistic geometry. The rate of fluid expulsion can also be incorporated into numerical models as the fluid source term.