Abstract: Aim\ To demonstrate the rationality and credibility of methods of computing curvilinear trajectories Methods The main equations of curvilinear trajectory and equations of curvilinear trajectory which consider second order approximation were computed by concentric spherical system Results The computational results show that there is a deviation about at the 5 th of decimal place between first and second order approximations of curvilinear trajectories, and aberrations computed for practica limaging tubes are about at the 4 th of decimal place Conclusion\ The computational methods of curvilinear trajectories have been proved