An important aspect of pre-flare current sheets in the solar atmosphere is the sudden enhancement of the effective electrical resistivity in the sheet due to the onset of a plasma micro-instability. Numerical and analytical solutions to the isothermal MHD equations are here presented that describe the evolution of a current sheet subsequent to such an enhancement in the resistivity. The solutions show that, if the initial width of the current sheet is less than the acoustic-diffusion length obtained by dividing the resistivity by the sound speed, then isomagnetic shocks are formed. These shocks propagate outward from the the centre of the current sheet and are transformed into fast-mode magneto-acoustic waves when they reach the edges of the current sheet. The fast-mode waves thus formed continue to propagate outward beyond the confines of the current sheet. In contrast to a previous study by Cheng, the present solutions demonstrate that flow speeds several times greater than the local fast-mode wave speed can be produced if the plasma beta parameter and the initial sheet width are sufficiently small. The results may be relevant to the triggering of a solar flare, as in the emerging flux model of flares.