A new mathematical model of hysteresis envelope of extended end-plate bolted beamto- column joint was developed in this doctoral thesis. The realistic assessment of steel moment resisting frame behavior under earthquake action by using a nonlinear static analysis was the main goal of this hysteresis envelope model. The model defined the ratio between the monotonic and cyclic behavior of the joint. The ratios are defined as a function of two parameters; the thickness of the end-plate and the vertical spacing between bolt rows at the end-plate. Moment resisting frame behavior obtained by using the new model of hysteresis envelope of the joint was compared with moment resisting frame behavior which takes into account the monotonic properties of joints. The nonlinear dynamic analysis of frames under real earthquake by using time histories was served as a verification method. A modified Richard-Abbott model that takes into account the degradation of strength and stiffness as well as the problem of pinching used to model the behavior of joint. In order to define the behavior of beam-to-column joint under earthquake action, a numerical finite element model was developed. The model takes into account geometric and material nonlinearities of the elementary parts of joint, preloaded bolts, and contacts between connected elements. The accuracy of the nonlinear finite element model was validated by experimental test available in references. To determine the cyclical properties of European mild steel S275 and S355, the experimental testing was conducted. To simulate the effect of variable strains which occurring in the structure under earthquake action, an experimental displacement control test of specimens was performed. Calibration of steel hardening parameters was performed following the Chaboche procedure to define the cyclic behavior with variable strain ranges. The Chaboche model takes into account a combined isotropickinematic hardening of steel. After the ultimate tensile strength of steel under the cyclic action was reached, a model of steel takes into account damage initiation and fracture. Such steel model which includes material hardening, degradation of strength and stiffness and damage was for the first time applied in the numerical model of joint.