Rapid mass transfer in a binary system can drive the accreting star out of thermal equilibrium, causing it to expand. This can lead to a contact system, strong mass loss from the system and possibly merging of the two stars. In low metallicity stars the timescale for heat transport is shorter due to the lower opacity. The accreting star can therefore restore thermal equilibrium more quickly and possibly avoid contact. We investigate the effect of accretion onto main sequence stars with radiative envelopes with different metallicities. We find that a low metallicity (Z<0.001), 4 solar mass star can endure a 10 to 30 times higher accretion rate before it reaches a certain radius than a star at solar metallicity. This could imply that up to two times fewer systems come into contact during rapid mass transfer when we compare low metallicity. This factor is uncertain due to the unknown distribution of binary parameters and the dependence of the mass transfer timescale on metallicity. In a forthcoming paper we will present analytic fits to models of accreting stars at various metallicities intended for the use in population synthesis models.