RESUMEN En este documento se desarrolló un método de análisis no lineal para la comprobación de columnas rectangulares esbeltas de hormigón armado y de acero rellenas de hormigón, cuyo objetivo fue calcular la directriz geométrica y mecánica de una columna para determinar, el máximo momento que puede resistir para una carga axial dada ya sea por agotamiento o inestabilidad. Palabras clave: Columna esbelta, pandeo, inestabilidad, agotamiento, radio de curvatura, directriz geométrica, directriz mecánica. ABSTRACT The design of reinforced concrete structural elements has improved over the years due to better knowledge of the behavior of its comprising materials. Columns as structural elements are very important in the structure life span. This paper develops a method for testing and analyzing nonlinear slender rectangular reinforced concrete columns and concrete filled steel columns, whose aim is to calculate the geometric and mechanical guideline of a column to determine the maximum moment which can withstand an axial load due to either depletion or instability. The method comprises an iterative process in which the neutral fiber depth and the radius of curvature. Graphics solutions (Guideline geometric and mechanical) that indicate the status of the last column were obtained. The method is versatile as it can be used to analyze columns consisting of different types of materials incorporating only stress-strain diagram; also the method is optimal as to check if a certain combination of column load resists, is not necessary to construct the interaction diagram. Keywords: Slender column, buckling, instability, depletion, radius of curvature, guideline geometric, guideline mechanical.