Electromagnetic force is a very important parameter for push-pull solenoids, but it is difficult to calculate analytically due to the nonlinear variation of the magnetic field. Aiming at this problem, To address this problem, this paper investigates the use of magnetic vector potential theory in a columnar coordinate system to solve the electromagnetic force of a cylindrical push-pull electromagnet. The whole solenoid magnetic field is divided into several sub-domains and the boundary conditions are defined to obtain the sub-domain magnetic vector equations which can be solved numerically, and then the electromagnetic characteristic data such as magnetic vector potential, inductance and electromagnetic force are calculated by MATLAB programming. Comparing the two cases of B-H curves of iron core permeability in finite element with constant value of 10000 and electric soft iron respectively, the calculation accuracy and error variation trend of this numerical algorithm are illustrated, and the reason for the formation of the error are analyzed. With the increase of current the core will be magnetically saturated, when the magnetic saturation problem is not serious, the calculation result of numerical algorithm has high accuracy; with the increase of current, the error increases rapidly after the core is magnetically saturated. In the experiment, different sizes of excitation currents were applied to the cylindrical push-pull electromagnet, and the output thrust results obtained were consistent with theoretical analysis.