Pump-turbines cope very well with modern electricity-market demand, having high operational flexibility and storage capabilities. Nevertheless, dynamic operation of these machines can lead to very challenging transient conditions, depending on the shape of the characteristic. Mechanical integrity can be correspondingly affected. Therefore, assessment of the characteristic during the design phase is of crucial importance. In the past years, different attempts to accurately compute the characteristic under steady and transient conditions have been undertaken using Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics. While the k–ω shear stress transport (SST) turbulence model has become the reference for machine design, it often fails for conditions close to or around instabilities. Under unstable conditions, which are characterized by continuous unsteady vortex formation, turbulence isotropy as assumed by linear two equation models is no longer the right choice. Accordingly, a turbulence model able to capture anisotropy, explicit algebraic Reynolds stress model (EARSM), has been implemented in an in-house code and used for the computation of the characteristic of various machines, stable and unstable, to assess the model performance. In this paper, computations of three different dynamic pump-turbine operating conditions are presented. Results using steady boundary conditions (BC) in the unstable region as well as transient BC like load-rejection and runaway are computed with EARSM, showing its superiority compared to linear two equation models. The model's capability to capture anisotropic effects—such as the influence of corners—produces more physical flow structures in the vaneless space, which lead to an overall improvement of the predicted stability characteristics.