Time-dependent structural serviceability problems have not been accord
ed enough attention. Of considerable interest in the present paper is
the structural response due to the creep and shrinkage effects of conc
rete material. This structural response is also highly uncertain and a
s such ought to be amenable to analysis using probabilistic methods. I
n this paper, based on mathematical models for both creep and shrinkag
e effects and applied load processes, two methods, namely a simulation
approach and an analytical approach, will be proposed to predict the
time-dependent serviceability of a simple reinforced concrete structur
e. The advantage of the simulation approach is that all the random var
iability can be included in the structural response at any point in ti
me, and in the analytical approach, the stochastic nature of the probl
em can be explored by using first passage probability and the Rice for
mula. An example is given to illustrate the approaches.