The hydraulic and thermal interaction between a vertical flat plate, either adiabatic or isothermal, and a rising thermal plume is investigated. The boundary layer equations are solved numerically by using finite difference method, with the wall boundary conditions changing from the Neumann to Dirichlet type as the free boundary encounters a flat plate in its course. For an adiabatic flat plate, the development stage of a new wall boundary from the impinging plume is elucidated. In the case of isothermal flat plate, study is made on the heat transfer which is complicated by the new wall thermal boundary layer developing within the already existing free boundary layer spawned by a horizontal line heat source. In all the cases, the initial disturbance by the existence of the flat plate is overcome and similarity solution for the wall boundary layer is asymptotically obtained downstream.