In this dissertation, the model of column subjected to displacementdependent non-conservative loads is studied in detail. The influence of Winkler s elastic foundation and elastic supports is carried out for some classical problems such as Beck s and Leipholz s. A methodology based on a matrix formulation is presented for determining the critical condition and load in a dynamic approach. The model developed is based on Rayleigh-Ritz method, using a combination of cubic polynomials and trigonometric functions to describe the displacement field of slender beam elements. This methodology was implemented in a computer program developed in MATLAB. The classical problems were used as numerical tests to evaluate the accuracy of this approach. Later, the analysis of elastic foundation and elastic supports influence are presented separately and together. It was possible to show that both critical load and its respective modes are affected differently for each type of elastic support and load distribution. Finally, the influence analysis of Beck s problem is compared to results presented in in bibliography of a model which includes fluid movement within the element. This comparison has the purpose to estimate a range of applicability of the classical Beck s model to a pipe conveying fluid.