A quasi-two-dimensional analytical model is developed to account for vertical and horizontal current flow in and adjacent to a square ohmic contact between a metal and a thin semiconducting strip which is wider than the contact. The model includes side taps to the contact area for voltage probing and relates the "apparent" interfacial resistivity to the (true) interfacial resistivity, the sheet resistance of the semiconducting layer, the contact size, and the width of the "flange" around the contact. This relation is checked against numerical simulations. With the help of the model, interfacial resistivities of ohmic contacts to GaAs were extracted and found independent of contact size in the range of 1.5-10 µm.