For many structures designed for high temperature applications, e.g. piping systems and pressure vessels, an important problem is the life time assessment in the creep range. The objective of this work is to present an extensive overview about the theoretical modeling and numerical analysis of creep and long-term strength of structures. The study deals with three principal topics including constitutive equations for creep in structural materials under multi- axial stress states, structural mechanics models of beams, plates, shells and three-dimensional solids, and numerical procedures for the solution of initial-boundary value problems of creep mechanics. Within the framework of the constitutive modeling we discuss various extensions of the von Mises-Odqvist type creep theory to take into account stress state effects, anisotropy as well as hardening and damage processes. For several cases of material symmetries appropriate invariants of the stress tensor, equivalent stress and strain expressions as well as creep constitutive equations are derived. Primary creep and transient creep effects can be described by the introduction of hardening state variables. Models of time, strain and kinematic hardening are examined as they characterize multi-axial creep behavior under simple and non-proportional loading conditions. A systematic review and evaluation of constitutive equations with damage variables and corresponding evolution equations recently applied to describe tertiary creep and long term strength is presented. Stress state effects of tertiary creep and the damage induced anisotropy are discussed in detail. For several structural materials creep curves, constitutive equations, response functions and material constants are summarized according to recently published data. Furthermore, a new model describing anisotropic creep in a multi-pass weld metal is presented. Governing equations for creep in three-dimensional solids are introduced to formulate initial-boundary value problems, variational procedures and time step algorithms. Various structural mechanics models of beams, plates and shells are discussed in context of their applicability to creep problems. Emphasis is placed on effects of transverse shear deformations, boundary layers and geometrical nonlinearities. A model with a scalar damage variable is incorporated into the ANSYS finite element code by means of a user defined material subroutine. To verify the subroutine several benchmark problems are developed and solved by special numerical methods. Results of finite element analysis for the same problems illustrate the applicability of the developed subroutine over a wide range of element types including shell and solid elements. Furthermore, they show the influence of the mesh size on the accuracy of solutions. Finally an example for long term strength analysis of a spatial steam pipeline is presented. The results show that the developed approach is capable to reproduce basic features of creep and damage processes in engineering structures.