Solving of large-scale systems of linear algebraic equations, ill-conditioned and non-square systems requires special algorithms which should be suitable for effective implementation in modern multi-processor systems. One of such methods was proposed by A.A. Abramov. This approach is based on consequential projecting of solution to a system of ortogonal vectors that are chosen by such mean that projections can be easily found. In this paper we discuss the main features and possible modifications of the Abramov method from the viewpoint of effective parallel implementation. The parallel Abramov algorithm and some results of its testing are also presented.