Demarcation of areal and linear seismic sources involves a certain degree of uncertainty and this should be reflected in the final seismic hazard results. The uncertainty associated with the description of the geographical coordinates of a source zone boundary is modeled by introducing the concept of 'random boundary', where the location of the boundary is assumed to exhibit a spatial bivariate Gaussian distribution. Here the mean vector denotes the best estimate of location and the variance reflects the magnitude of location uncertainty, which may be isotropic or may show spatial directivity. The consideration of spatial randomness in the boundaries smooths the seismicity parameters and permits the gradual transitions of these to occur across border zones. Seismic sources modeled as lines can also be attributed random geometrical properties.