Modelling of frictional devices is one of the greatest remaining problems in structural mechanics. The dissipative properties of frictional interfaces are central in design and analysis of built-up structures such as engines, aerospace structures and bladed-disk assemblies. These interfaces exhibit complex, nonlinear behavior and are the main source of uncertainly in finite element models for built-up structures. It is shown that the frictional interfaces are the main cause of damping and challenges in predicting the dynamic characteristics (stiffness, mode shapes, ...) of a systems containing interfaces. Improved methods for modeling joints have been presented recently, however, numerical computation of the dynamic behavior of a system containing interfaces can be excessively expensive due to the nonlinearity introduced by the interfaces. The resulting simulations are still quite expensive, often impractical for a system that contains many joints, and none of the simulations has been thoroughly validated against measurements. Especially, when a dynamic simulation is implemented, the computational cost becomes completely prohibitive since the response must span many cycles of oscillation. Indeed in most practical applications, the inertial terms can be neglected in a local sense (i.e. near the joint) since accelerations in those regions are small relative to elastic forces, which makes the implementation of quasi-static methods logical. The primary contribution of this work is the development and validation of novel quasi-static methods for modeling and analyzing the dynamic response of structures that contain frictional interfaces. The work seeks to answer the following questions: Are quasi-static methods effective to predict the dynamic characteristics of a nonlinear system? Are the results obtained using quasi-static methods verifiable against measurements? Are they applicable to complex and realistic systems containing many joints? How much efficiency is provided by using quasi-static methods instead of dynamic methods? What are the limitation of using quasi-static methods to be implemented as an alternative to the dynamic methods? Are the proposed quasi-static methods applicable for a nonlinear system subjected to harmonic forces? If quantitative predictions of quantities such as the nonlinear Frequency Response Functions are desired, at what level can the proposed quasi-static methods be used effectively? To address these concerns, several quasi-static methods are proposed in this thesis for different systems involving interfaces subjected to harmonic or random dynamic forces. The results obtained are verified against experimental measurements, the advantages of the proposed methods as well as their limitations are investigated, and the computational cost of these methods are compared with the alternative methods. Examples are presented in which the proposed quasi-static methods are demonstrated as feasible, efficient methods in order to predict the dynamic features of built-up systems including frictional devices.