This paper presents an approach for calculating first excursion probabilities of linear structural systems subject to stochastic Gaussian loading. This probability is estimated by multidomain Line Sampling, which is an advanced version of the classical Line Sampling approach, capable of dealing with multiple failure criteria. Multidomain Line Sampling exploits the linearity of the structural system with respect to the loading. Thus, it is possible to estimate small failure probabilities (within the range of 10−3) with high precision and efficiency. These characteristics are illustrated by means of a numerical example.