Abstract: This paper shows a new finite element algorithen of the plane rigid-jointed frames of non-even variable section fo resonance on arbitrary boundary conditions. Seine the problems are summing up as the variable coefficient differential equations with non-positive property, it is difficult to solve the equations of the problems by the calculus of variations, this new algorithm derives the stiffness matrix of elements for the arbitrary variable section member of the rigid-jointed frames based on the differential equations of the problems. This algorithm has many good points. First, the computation times and the memory quantities are reduced in the course of the computation. Next, the accuracy of the computation results is increased. The compution resilts show that this algorithm is accurate and feasible in the examples.