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In this project the slip effect on free convection of a Casson fluid past an infinite oscillating vertical plate with constant wall temperature is investigated. It is used to characterize the non-Newtonian fluid behavior. By introducing appropriate nondimensional variables, the resulting equations are solved analytically by using the Laplace transform technique. The corresponding solutions for a Casson fluid without slip at the boundary for ! 0, a Newtonian fluid with slip for Gamma ! 1, and a Newtonian fluid in the absence of slip for ! 0 and Gamma ! 1 are obtained as limiting cases. The influence of the slip parameter and Casson parameter cause a decrease in the velocity field. Numerical results for velocity, temperature, Nusselt number and Skin fraction are shown in various graphs and discussed for the embedded flow parameters.