Dynamical behavior of particles in a Paul trap in the presence of damping force has been investigated. Position of trapped ions as a function of time, ion trajectories and the phase space curves considering the effect of the damping force were obtained. Four regions of stability for r and z components with the damping force as well as the maximum value of q when U=0 for the first region, namely q max , versus damping factor k were computed using the fourth-order Runge–Kutta method. Comparisons were made with the corresponding stability diagrams without the damping force effect recently published in the literature. The third and fourth stability regions in the presence of the damping force, the curve of q max as a function of k and the related equation are reported for the first time.