A large number of studies have shown that nonlinear passive control devices have good vibration attenuation and isolation effect. And vibration isolation systems with nonlinear stiffness have more advantages than linear systems. The paper addresses the stiffness and load capacity design problem of Euler springs with varying cross-sections. Firstly, in order to analyze nonlinear behavior of curved beams due to large geometric deformations, a set of first-order differential equations are established, which can be easily solved by numerical integration. Secondly, a curved beam is taken for example to compare analytical results calculated by using the first-order differential equations and ANSYS simulation results. Then the influence of geometric parameters of curved beams with varying cross-sections on structural stiffness and load capacity is investigated by using ANSYS. Finally, a design strategy for stiffness and load capacity of curved beams is summed up.