In this thesis, an estimation of limit load in frame structures has been considered. Calculations are conducted both analitycally and numerically using the software package Abaqus, which employs the Finite Element Method (FEM). In the introduction, the methods for estimating the limit load in frame structures and the behaviour of elastic – perfectly plastic material are presented. In the second chapter, the Finite Element Method (FEM) and the software package Abaqus are described. In adition, the finite elements used in this thesis are further elaborated. The third chapter deals with the verification of the finite elements and modeling techniques applied in this work. The results have been verified by studying a beam subjected to pure bending and torsion. The comparison of the results obtained by two–dimensional plane stress elements and three–dimensional hexahedron „brick“ elements is presented. Thereby, both the first- and the second-order elements has been tested. The analysis has been carried out for a elastic–ideally plastic material, by assuming the small strains and displacements. In the numerical calculations, the elasto – plastic analyses is conducted by emplyoing incremental techniques in order to determine the spreading of the plastic areas and the limit condition of the frame structures. In all of the calculations, the numerical solutions were obtained by available analytical results. In the fourth chapter, the analytical and numerical analysis of frame structures are presented. For the given two-dimensional frame structure, the limit load is estimated analitically by using the lower and upper bound theorems of the limit analysis, as well as the rigid plastic hinge approach, while in the numerical the elasto-plastic analysis was preformed in order to analize the spreading of the plastic areas and to estimate the limit load of frame structures. For the given space frame structure, the analytical elastic analysis is carried out in order to determine the lower bound of the limit load. Thereafter, the numerical easlto-plastic analysis is conducted in order to estimate the limit load of the frame structure.