Two thermomechanical models of pure metal solidification on a sinusoidal mold surface are developed using a linear perturbation technique. In the first model, the mold surface temperature is held constant; while in the second model, the heat flux through the mold-shell interface is held constant. In both cases, the ratio of the mold surface amplitude to the wavelength is taken as the perturbation parameter and the models are thus limited to low aspect ratio surfaces that are perfectly wetted by the molten liquid. Mechanical distortion of the metal shell due to nonuniform heat flow through the spatially oscillatory mold-shell interface causes a change in the contact pressure along the interface. Both models show that the contact pressure increases at the crests of the mold surface while simultaneously decreasing in the troughs. This suggests a possible growth instability since micro-air gaps may nucleate in the mold surface troughs rather than at the crests, thereby reducing heat extraction beneath the thinnest regions of the shell and exaggerating its undulatory macromorphology. A method for generalizing both models for an arbitrary periodic mold surface topography, f( x), is also presented. Finally, the surface waviness of the metal shell is calculated after solidification ends and the shell is released from a mold with a purely sinusoidal surface topography.