In this paper, an algorithm for researching the stability of linear systems using a computer is proposed. The stability of systems with delay is reduced to finding the limit conditions for the negatives of the real parts of the zeros of the corresponding quasi-polynomials. Verification in practice of such conditions is possible only in the simplest cases. The algorithm proposed in this paper is based on schemes for approximating linear systems with a delay by used sequence special of systems of linear ordinary differential equations. The equivalence of the exponential stability of systems with delay and of the proposed system of ordinary differential equations is established. This allowed us to build an algorithm for studying the location of non-asymptotic roots of quasi-polynomials, which are implemented on a computer.