A linear theory for pretwisted elastic beams subjected to general loads is developed from the potential energy functional. The longitudinal strain distribution is that of a similar beam without pretwist supplemented by terms from the warping function and its longitudinal derivative. The paper contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent asymptotic result from three-dimensional elasticity apart from the limitation imposed by neglecting deformations of the cross sections in their own plane.