The investigation presented in this work concerned one-dimensional modelling of transient flow in an axial turbine stage. Because of the compound motion in the rotor-blade channels, the model of this flow path element was considered the most difficult to solve. The basic modelling approaches and the usefulness of the Euler and Lagrange methods for mathematical description are discussed. Relevant applied model based on the Lagrange method is described. Results of a successful numerical simulation of transient flow in a turbine stage are presented. This success opens the opportunity to build and solve one-dimensional models of dynamic flows in turbine cascades and entire flow paths.