In this study, the effects of buoyancy and conjugate heat transfer flow over a vertical plate embedded in a porous medium have been investigated. The plate has a finite thickness and one side is held a finite temperature. In order to determine the velocity and temperature distributions in the flow area, the equations of Navier-Stokes and energy are transformed into the boundary layer equations using the similarity method. Then these equations solved numerically using the Keller box method. The effects of the conjugate heat transfer and the buoyancy parameters on the velocity and temperature profiles as well as on the local skin friction and local heat transfer are determined. Testing the accuracy of the numerical method, the results are compared with those available in the existing literature and an excellent agreement is obtained.