The focus of this study is on numerically investigating the effects of additive noise on the dynamics of vibro-impact oscillators with compliant supports. Various models for the compliant supports have been considered, which include elastic, elasto-plastic, linear and nonlinear dissipative contact force models, and which follow constitutive laws that are discontinuous. It has been shown that noise superimposed on the harmonic excitations alters the dynamical features of the non-smooth systems significantly. Stochastic bifurcation analyses have been carried out to investigate the stability characteristics of the systems with respect to the different compliant force models and a comparison has been presented on the advantages and limitations of the various contact force models in the presence of noisy excitations.