A prism coupler filled with nonlinear Kerr-like material is studied theoretically. A simple, approximate analysis is developed to predict its behavior in both linear and nonlinear optics. In a wide range of incident amplitude magnitude, optical bistability and multistability are found. As far as field map not undergo drastic change, the simpler approximate theory is able to quantitatively analyze both prism couplers and waveguide in nonlinear optics and to study such effects as nonlinear phase shift, existence of nonlinear asymmetric modes in symmetric environments, bi-and multistability. The predictions of the analytical theory are compared with the results obtained via numerical integration of Maxwell equations and they agree quite well.