We study the effect of interchain coupling on the Peierls transition temperature TP for a model with a nonplanar Fermi surface. Using the standard electron-phonon coupling, we show that the soft mode which causes the transition should have a wave vector q0=(πa,πa,2pF). We evaluate the effect of interchain coupling on TP within the mean-field theory, as well as the effect of fluctuations. Both these effects reduce TP, but we find that there is a range of interchain coupling where this reduction, due to both effects, is small. Neutron-scattering cross section and fluctuation contribution to the specific heat are evaluated. Comparison is made with experiments on K2Pt(CN)4Br0.3•3H2O (KCP) and tetrathiofulvalene-tetracyanoquinodimethan (TTF-TCNQ).