This thesis is about a linear stability analysis for the lid driven cavity problem.The system of choice consists of a two dimensional rectangular box in x- and y-direction, extended to infinity in the 3rd dimension (z-axis). The top lidof the box is moving tangentially to itself with a constant velocity and an inclination angle with respect to the x-axis in the z-direction. In this thesisa Python program using the FEniCS library is written to simulate the flowand perform a stability analysis. The lid driven cavity is a benchmark systemdue to the simple rectangular geometry and therefore much theoretical workhas already been done, which allows to test the written code and assure thecorrectness of the results. A linear stability analysis is carried out and the criticalReynolds numbers are determined as functoins of the cross-sectional aspectration and the direction of lid motion. The energy budget of critical modes isanalyzed using the Reynolds-Orr equation. For some parameter combinations,new modes are found at lower Reynolds numbers than already published results.The correctness of the present results is verified by full 3-dimensionalflow simulations.