The adsorption of dimer molecules onto finite width surfaces is studied using an Ising model approach. The energy of the system is calculated recursively by accounting for every possible lattice configuration. From the energy recursion, the grand partition function is calculated exactly and all thermodynamic properties of the system can be derived. For attractive interactions at a given temperature and chemical potential, lattice coverage increases monotonically with lattice width. This behavior corresponds to an increase in entropy due to an increase in possible configurations. For repulsive interactions, substeps in the adsorption isotherm are observed for all lattice systems. The number and corresponding density of the substeps are dependent on the lattice width and occur at configurations that minimize the system energy. The substeps are a strong function of temperature, and become more pronounced as the temperature is decreased. The results for systems with repulsive interactions are consistent with previous findings for compression in adsorbed layers.