Abstract: This paper is concerned with the time-varying body whose shape varies with time. By combining time-varying mechanics and damage theory, basic equations and numerical equations of visco-elastic-plastic time-varying damage mechanics are given. By computer simulation of mining process of one underground coal bed, dynamic evolution of damage field and surface subsidence due to shape varying is obtained. The spatial displacement evolution of time-varying body is analyzed quantitatively and the path correlation characteristic is studied. By time-varying damage analysis, continuous evolution of damage and displacements is obtained. Different construction path will cause different final property state, which is called the phenomenon of “path correlation”. It is found that the ultimate state of construction is generally related to construction path in nonlinear material widely, which is of applied and theoretical value in engineering analysis and academic research.