Nowadays, with the help of developing technology, engineering problems which are difficult to solve have become easily solved in a short time by means of computer software. Certain mathematical algorithms are used in these analysis methods. The mathematical and numerical solution methods created provide a significant solution facility for engineering. In this paper, the buckling analysis of the Euler column model, with elastic boundaries and containing steel fibers, under pressure effect is performed. In the column model, three different sections, which have been produced from four different concrete series, including three different types of fiber reinforced specimens and one non-fibrous control sample(C) with 0.6% by volume, were analyzed by using a software. In the study, the analysis of the critical buckling values depends on length, elastic modulus and cross-sectional type of the column model has been performed. The results are shown in graphs and tables. With the results of the analysis, the effect of slenderness and steel fiber concrete on the critical load in pressure columns have been investigated.