A thermodynamic finite-strain model describing the pseudoelastic response of shape memory alloys is proposed. The model is based on a self-consistent Eulerian theory of finite deformations using the logarithmic rate. Purely elastic material response is derived from a hyperelastic potential. The mass fraction of martensite is introduced as internal state variable to indicate the thermomechanical state of the phase transforming material. The evolution of martensite is governed by a kinetic law which is derived from the Helmholtz free energy of the two-phase solid and takes the heat generated during phase transition into account. The material model is implemented into a finite element code in an updated Lagrangian scheme and calibrated to experimental data. Simulations under different loading conditions illustrate the characteristics of the model.