A novel semi-analytical method is proposed to develop the pseudo-rigid-body~(PRB) model of robots made of highly flexible members (HFM), such as flexures and continuum robots, with no limit on the degrees of freedom of the PRB model. The proposed method has a simple formulation yet high precision. Furthermore, it can describe HFMs with variable curvature and stiffness along their length. The method offers a semi-analytical solution for the highly coupled nonlinear constrained optimization problem of PRB modeling and can be extended to variable-length robots comprised of HFM, such as catheter and concentric tube robots. We also show that this method can obtain a PRB model of uniformly stiff HFMs, with only three parameters. The versatility of the method is investigated in various applications of HFM in continuum robots. Simulations demonstrate substantial improvement in the precision of the PRB model in general and a reduction in the complexity of the formulation.