We present a linear stability analysis of Horton-Rogers-Lapwood convection in an anisotropic porous, medium bounded by finite-property plates of infinite horizontal extent. Critical values for the onset of convection are obtained using a continuation method. These values are compared with experimental data. The effects of plate diffusivity, plate diffusivity, plate thickness, and anisotropy in the diffusivity and permeability of the porous medium on these critical values are explored. We find that the predicted critical values from our stability analysis agree favorably with available precision experimental measurements.