In the present paper, we have examined the flow of Williamson fluid in an inclined channel with pressure dependent viscosity. The governing equations of motion for Williamson fluid model under the effects of pressure dependent viscosity and pressure dependent porosity are modeled and then solved numerically by the shooting method with Runge Kutta Fehlberg for two types of geometries i.e., (i) Poiseuille flow and (ii) Couette flow. Four different cases for pressure dependent viscosity and pressure dependent porosity are assumed and the physical features of pertinent parameters are discussed through graphs.