The course introduces finite element methods for the analysis of problems of linear elasticity. The course starts with Galerkin finite element method formulation of static problem for linear elastic 1D body. Later the FEM is theory is generalized for 2D case. 3D case, linear fracture mechanics, transient, and dynamic conditions, heat transfer problems, etc. will be discussed. Finite element method is presented using largely physical arguments. Students are supposed to develop their own FEM implementation for 1D and 2D problems of elasticity using PYTHON programming language. Part of the course and course homework involves utilization of general-purpose finite element analysis program ANSYS including development of simple APDL (ANSYS parametric design language) subroutines for automation of solution obtaining. Applications include finite element analyses, modelling of problems, and interpretation of numerical results.