Based on the need for effective solutions of structures response to seismic loading, this thesis includes the theoretical background, and explanation of several methods. There are many theories in the community, but the ones chosen to be looked closer at here are Modal response spectrum analysis for symmetric and asymmetric plan structures, Modal Pushover Analysis for symmetric and asymmetric plan structures and Linear and Non-Linear Response History Analysis. The theory has been adapted from published papers and books on the topic.The report is divided into three main sections, numerical methods for solving of dynamic problems, elastic analysis and inelastic analysis. The chapters on Elastic and Inelastic analysis are further divided into sections on symmetric and asymmetric plan.Elastic analyses by hand calculations and SAP2000 have been performed on a 2D-frame, aSAP2000 Elastic Response spectrum analysis has been performed on a 3D-frame, and aninelastic modal pushover analysis in SAP2000 has been performed on a 2D frame.The target for this inquiry is to discover advantages and disadvantages in the different methods and comparing them.