The Signorini problem with friction in quasi-coupled linear thermo-elasticity (the 2D-case) is discussed. The problem is the model problem in the geodynamics. Using piecewise linear finite elements on the triangulation of the given domain, numerical procedures are proposed. The finite element analysis for the Signorini problem with friction on the contact boundary ${\Gamma }_{\alpha }$ of a polygonal domain $G\subset R^2$ is given. The rate of convergence is proved if the exact solution is sufficiently regular.