We study the voltammogram spikes of the underpotential deposition at electrode surfaces that correspond to first-order phase transitions. The shape of symmetric spikes is approximated by the function cosh(-2). In order to explain this spike shape microscopically, which is our main concern, we observe that an electrode surface consists of many small crystals. A voltammogram spike is then interpreted as an averaged result of the finite-size effects occurring in each of these crystals. This view also allows us to comment on asymmetry in the voltammogram spikes. Our analysis is based on the rigorous statistical mechanical techniques of the Pirogov-Sinai theory. For the sake of simplicity, we model the deposition process by the one-component lattice gas. We apply the results to the underpotential deposition of Cu on Pt(111) in a sulfuric acid medium, and find very good agreement with experiment.