The present work is concerned with the development of finite element techniques for nonlinear transient dynamic analysis of reinforced concrete plates and shells. Computational models have been developed and coded, which are applied to various engineering problems under static and dynamic loading conditions. The first part of the thesis deals with some aspects of linear-elastic, geometric and material nonlinear finite element formulations of general thin and thick shell analysis under static or quasistatic loading. A generalized displacement method is proposed to overcome the 'shear locking' problem for the degenerated thick shell element when used in the context of thin shell structures. The basic concept and mathematical formulation of the generalized displacement method are detailed and its application is illustrated by numerical examples. The method is also extended to the geometrically nonlinear analysis of thin shells based on both Updated and Total Lagrangian formulation. An elasto-viscoplastic analysis of anisotropic plates and shells is developed by means of the finite element displacement method. A discrete layered approach is adopted to represent different material properties and gradual plastification through the thickness. Viscoplastic yielding is based on the Huber-Mixes criterion extended by Hill for anisotropic material and special consideration is given to the evaluation of the viscoplastic strain increment for anisotropic situations. The second part of this thesis is concerned with nonlinear dynamic transient analysis of reinforced concrete shell structures. Direct integration methods are reviewed and discussed. In particular, the general single step explicit, implicit and implicit-explicit algorithms with predictor - corrector forms are presented and corresponding stability conditions are deduced by invoking the energy method. The modelling of reinforced concrete behaviour in shell structures under fast loading conditions is considered. Both a strain rate sensitive elasto-viscoplastic model and a strain rate sensitive elasto-plastic model are presented for describing concrete nonlinearities due to multiaxial compressive or tensile yielding under dynamic loads. The models are used in conjuction with a tensile crack monitoring algorithm to trace concrete crack opening and closing. Various reinforced concrete plates and shells are analyzed and reported in detail, with the results obtained being compared with those from other sources.