The effects of electron Rutherford scattering on the Weibel instability are investigated using the implicit plasma simulation codevenus[J. Comput. Phys.46, 271 (1982);63, 434 (1986)]. Collisions decrease the Weibel growth rate below the collisionless value, in agreement initially with simple linear theory. Likewise, collisions decrease the saturation level, in agreement with a magnetic trapping mechanism. When the collision rate exceeds the collisionless Weibel growth rate, the instability is suppressed altogether. The results provide benchmarks for analysis of proposed short‐wavelength laser‐fusion schemes.