This paper presents a theoretical description of a particle motion in a rotary dryer equipped with straight lifters distributed on its periphery. In this configuration, the transport of granular materials occurs with cyclic cascades that can be decomposed into three phases: lifting, discharging, and falling into the air stream. In order to describe each of these phases, we have focused on the motion of a single particle in a rotating drum. In this condition, the analytical solution of the motion equation of each phase is found. With these solutions, the position and the velocity of the particle at any time are thus expressed as a function of physical parameters of the particle, physical parameters of the drum, and physical parameters of air in the drum, called operating parameters in practice. With these equations, we are able to calculate the behaviour of the particle as a function of the operating parameters. The transposition to the industrial context is made with an application. We show how these equations particularly permit the estimation of the Mean Residence Time (MRT) of material during the drying process as a function of operating parameters. Such estimations have been validated by comparison with experimental data of MRT found in the literature. The work presented in this paper gives some useful mathematical relations for whose who are interested in drum design optimization (lifter length, drum radius, drum length, etc.). More specifically, they can be used to help with the choice of operational parameters values that would achieve a given value of MRT for particular product.