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When a poroelastic gel is released from a patterned mold, surface stress drives deformation and solvent migration in the gel and flattens its surface profile in a time-dependent manner. Specifically, the gel behaves like an incompressible solid immediately after removal from the mold, and becomes compressible as the solvent is able to squeeze out of the polymer network. In this work, we use the finite element method (FEM) to simulate this transient surface flattening process. We assume that the surface stress is isotropic and constant, the polymer network is linearly elastic and isotropic, and that solvent flow obeys Darcy's law. The short-time and long-time surface profiles can be used to determine the surface stress and drained Poisson's ratio of the gel. Our analysis shows that the drained Poisson's ratio and the diffusivity of the gel can be obtained using interferometry and high-speed video microscopy, without mechanical measurement.