The simplified strain gradient elasticity theory (SSGT) is used to study the induced flexoelectric effect in an anisotropic dielectric beam due to bending. The beam cross-sections are uniform with internal cubic structure symmetry. Three different cases are studied in the context of the Timoshenko beam theory. In the first two cases, the simply supported beam subjected to uniformly distributed or graded forces at the lateral surface of the beam are considered, while the third case is devoted to study the clumped-free ends beam problem subjected to graded force. With appropriate boundary conditions, a closed-form solution is obtained for the problem filed equations. The study shows that, when the applied force is concentrated at the center region of the beam, the induced spontaneous polarization is directed towards the beams two ends. While, when the beam is clamped from one end, the induced spontaneous polarization moves towards the applied force.