Estimating the nonlinear resonance of structural systems with contact boundary is critical for design, control, and health monitoring of mechanical and aerospace systems. The nonlinearity caused by the intermittent contact excludes the use of traditional linear analysis methods. In this research line, we propose analytic-based approaches to enable efficient prediction of resonant frequency, transient response, and steady-state response of structures with contact nonlinearity. Computational savings of several orders of magnitude can be achieved using the proposed techniques.