Abstract New techniques of preparing thin semiconductor samples of uniform thickness have been developed, which allow for high sensitivity in the measurement of surface effects. Measurements of the surface transverse magnetoresistance effect first reported by Z emel and P etritz have been extended to lower resistivity n-type material of different crystallographic orientation. Data were obtained for directions of the magnetic field both in and perpendicular to the plane of the thin films. Large swings in surface potential were accomplished by employing an HF rinse prior to ambient cycling. Observations of surface transverse magnetoresistance effects as a function of surface potential at fixed magnetic field strengths, and as a function of magnetic field strength at fixed surface potentials are reported. The analysis of the data requires a general solution of Poisson's equation which does not employ the semi-infinite geometry in order to ascertain values of the electric field at the surface of a semiconductor. This general solution is presented for several special cases of sample thickness and resistivity and the deviations from the semi-infinite geometry solutions are delineated. Finally, the observations of the surface transverse magnetoresistance effect are discussed in view of the present theoretical model of the surface.