Due to the electrochemical nature of almost all corrosion reactions, electrochemical methods are commonly used to measure the corrosion rate of a metal in the laboratory or in the field. In particular, steady state methods are the most widely used for corrosion rate measurements. Transient methods, which can be much more efficient, traditionally rely on an equivalent linear circuit representing the surface kinetics, with negligible mass transport effects. This has been reported to predict transients which are not observed experimentally in many practical situations, in this paper, we consider the galvanostatic method, wherein a constant current is applied across a corroding metal surface and the transient potential response is recorded. The resulting boundary value problems incorporating mixed kinetic and diffusion control involve highly nonlinear, coupled boundary conditions. We present numerical and approximate analytical solutions which can be incorporated into corrosion analysis routines in order to calculate corrosion parameters. The analytical expressions open the possibility of measuring corrosion parameters by merely fitting a class of elementary functions to experimental potential transients. This leads to a significant reduction in the number of computations required for the curve fitting, and hence increasing the overall efficiency of the measurement process compared to the conventional steady state methods.