Designing and constructing of road embankments, deep excavations, landslide and snow avalanche predictions or profiling construction sites in slanting terrain need slope stability evaluations. Determination of a safety factor and the position of a potentially critical slip surface is one of the essential issues in classical and modern soil mechanics, which still remains a very important problem in engineering practice. Most of the stability evaluation methods, i.e. based on limit equilibrium assumptions, need optimization, which can be successfully realized with the assistance of a genetic algorithm. The authors propose a variational approach with a four-step technique to determination of the critical height of a slope, which can be treated as an alternative and variant method to the generally applied limit equilibrium and/or finite element methods. Some common obstacles encountered while adapting classical optimization procedures have been solved by application of a parallel genetic algorithm. Substantial acceleration of computations has been achieved by introducing SIMD stream technology, which generally relies on modern graphics processing units. Examples of the results of a slope stability analysis performed using the fast parallel computation technique are also presented.