The familiar small strain thermodynamic 3D theory of isotropic pseudoelasticity proposed by Raniecki and Lexcellent is generalized to account for the geometrical effects. The Eckard-Mandel concept, of mobile isoclinic reference configurations, is used for multiplicative decomposition of total deformation gradient into elastic and phase transformation part and resulting from it additive decomposition of Eulerian strain rate tensor. As a set of state parameters entering macroscopic free energy function of SMA material in actual configuration logarithmic elastic strain, temperature and mass fraction of martensitic phase is used. There will be presented selected experimental results for support of adopted theoretical assumptions. In finite deformations theory we will adopt without a "proof" a number of concepts from small strains theory. For example, in small strains theory of pseudoelasticity it can be proved that parent phase reaches unstable absolute equilibrium states when thermodynamic driving force of phase transformations (p.t.) becomes zero. This gives merit for requiring that p.t. can start when thermodynamic driving force of p.t becomes zero. The same condition is adopted in the finite deformation theory without formal support. The rate equations for SMA material formulated in the mobile Lagrangian configuration are translated to the actual configuration. They are relevant for the use of updated Lagrangian technique. Their combination with the nominal rate of stress tensor (by familiar bridging equation) and rate form of equilibrium equations leads to the fundamental set of partial differential equations of pseudoelasticty for the velocity field. Since SMA materials exhibit small elastic distortions but possibly large elastic dilatational changes, e.g. under dynamic loads. The postulated here elastic shear strain energy has the same functional form as the one used in small strains theory but upon substitution of small strain tensor with logarithmic strain

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