To study diamagnetic and compressibility effects for stellarators, toroidally averaged equations describing resistive pressure‐driven modes are developed. Linear stability results are given for cylindrical geometry and toroidal geometry. When toroidal coupling is included, both the analytical theory and numerical calculations show that diamagnetic effects can be destabilizing when they are small. However, for parameters appropriate to the Advanced Toroidal Facility (ATF) experimental device [J. F. Lyonetal., Fusion Technol.10, 179 (1986)] the diamagnetic effects are large and stabilizing. The linear results also show that for the specific cases reported here compressibility effects tend to cancel toroidal effects. Cylindrical calculations which include diamagnetic effects may then be adequate for the study of the experimental data.