Abstract This paper investigates the axial-torsional coupled vibration of a drill-string under combined deterministic and random excitations. Finite element method (FEM) is used to model the system. The random excitation at the bit-rock interaction, which is considered in the bit axial direction, is treated as Gaussian white noise. Statistic linearization is first applied to find a equivalent linear dynamic system which is then solved with stochastic Newmark algorithm. The statistics of the responses, including the means and standard deviations of the bit axial displacement and rotational velocity are obtained and analyzed.