For thin elastic films of crosslinked polydimethylsiloxane (PDMS), the tensile modulus was found to be an increasing function of reciprocal thickness over the whole range of elongations. PDMS films between 0.052 and 0.018 mm were investigated. With decreasing film thickness, surface properties may be expected to increasingly contribute to the measured modulus. For small elongations, surface tension is expected to have no effect or to decrease the measured modulus compared with that of a hulk sample. If a surface layer with a modulus greater than that of the bulk modulus is assumed to exist, then the observed increase in modulus with decreasing film thickness can be explained.