The total strain energy release rate of a homogeneous orthotropic cracked beam-like structure is calculated using Timoshenko's beam theory. The total strain energy release rate is modified by including the energy spent in the deformation of the beam near the crack tip. The contribution due to the root rotation is obtained by solving an approximately equivalent 2-D elasticity problem. By including the contributions due to the root rotations of the beam segments during crack extension, the modified beam model prediction of strain energy release rate is shown to agree very well with the 2-D finite element results.