In geomechanics there are problems whose investigations lead to solving model problems based on variational formulations. Such problems are frequently formulated by variational inequalities as they physically describe the principle of virtual work in its inequality form. In the first part of the contribution the algorithm for the numerical solution of the discussed variational inequality problem will be investigated. The used parallel algorithm is based on a nonoverlapping domain decomposition method for unilateral contact problem with the given friction and the finite element approach. The conditions of solvability will be presented. In the second part of the contribution a unilateral contact problem with friction and with uncertain input data in quasi-coupled thermo-elasticity is analysed. Method of worst scenario will be applied to find the most “dangerous” admissible input data. The solvability of the corresponding worst scenario (antioptimization) problem will be shortly discussed. Numerical experiments, e.g. a tunnel crossing by an active fault will be presented.