This chapter presents the methods of determining damping coefficients and response analysis of multiple degree-of-freedom systems. The damping matrix can be symmetric or nonsymmetric, proportional or nonproportional. For nonproportional damping, the response analysis involves complex eigensolutions. Viscous damping can be classified as proportional or nonproportional damping. The chapter discusses the response analysis technique for the former. It explains how to identify a damping matrix by whether it is proportional or not. The chapter examines the iteration method, which is a general complex eigensolution technique for multiple degree-of-freedom systems. Also included is the proof of orthogonality condition and the iteration for higher modes. In order to converge to the next higher mode by iteration, the complex trial vector must be orthogonal to the previous eigenvector and it’s conjugate. The iteration procedures for complex eigensolutions can be applied to undamped, proportional damping, and nonproportional damping.