An analytical cross-phase modulation (XPM) model is developed for coherent fiber-optic transmission systems. The XPM fields are calculated using a first-order perturbation theory. Statistical analysis is then applied to calculate the XPM variance. The analytical XPM model is applicable to dispersion-managed fiber-optic systems with arbitrary pulse shapes. For non-Gaussian pulses, a summation of time-shifted Gaussian pulses is used to fit the target pulse shape, which makes it possible to analytically derive the XPM variance. The analytical XPM model is validated by extensive numerical simulations.