Reinforced concrete is a very complex material in structural construction.Even the concrete strength will increase in early time, with the time change this strength usually decreases.Also the steel strength in reinforced concrete will decrease with time variation.However, for a long time the time-dependent property of construction materials has not been considered importantly in design and research of structure engineering.In this paper the time-dependent resistance models on concrete and steel decrease strengths are introduced.If the initial strength of concrete increased can be neglected, the time-dependent strength of concrete and steel in reinforced concrete can be composed by means of a time variable function and the initial strength. The probability characteristic of earthquake occurrence should be considered for analyzing aseismic structure.In a certain period the time, space, number and intensity of earthquake are all random variables.The general method for evaluating earthquake effect is an analysis procedure of earthquake risk.The safety probability of structure under the earthquake effect can be expressed by a probability integral.The integral functions are composed by the failure condition probability of structure and probability density function of maximum earthquake parameter. Structural dynamic response of earthquake effect actually is a non-stationary stochastic process, which can be simplified as a stationary process.Under this assumption the vibration equation of multi-degree freedom structure can be analyzed by the mode superposition method.Usually, the earthquake acceleration expressed by the time function and a stationary process should be considered in random dynamic response of earthquake acting on construction structures. To insure "no failure under small earthquake effect", the capacity of aseismic structure within the elastic region is studied, and first passage failure model is applied.If the passage event meets the Poisson assumption then the reliability integral can be expressed simply. It is significant for the analysis of criterion, mechanics and index of failure in structural reliability evaluation. In this paper two typical failure criteria are proposed: one is random time dependent strength criterion, and the other is time dependent deformation criterion.Both failure criteria can be used as the boundary of reliability analysis in construction structures.The whole reliability of time-dependent structure is also studied in this paper. Finally, an engineering structure example is given.The time dependent reliability is computed and the results show that if the action time of earthquake is short, then the maximum shears between layers of the structure are used as load response.The shear resistance of the structure appears obviously decreased with the time change.In this example several different kinds of boundaries are given by computing the time-dependent reliability. The method and theory introduced in this paper give a practical way to evaluate the reliability depending on the time variation.