Structures are subject to changing loads from various sources. In many instances these loads fluctuate in time in an apparently random fashion. Certain loads vary rather slowly (called constant loads); other loads occur more nearly as impulses (shock loads). Suppose that the stress put on the structure by various loads acting simultaneously can be expressed as a linear combination of the load magnitudes. In this paper certain simple but somewhat realistic probabilistic load models are given and the resulting probabilistic model of the total stress on the structure caused by the loads is considered. The distribution of the first time until the stress on the structure exceeds a given level x, and the distribution of the maximum stress put on the structure during the time interval (0,t) are studied. Asymptotic properties are also given. It is shown that the asymptotic properties of the maximum stress are related to those of the maxima of a sequence of dependent random variables. Classical extreme value type results are derived under proper normalization.