The present paper deals with the resolution on cloud architecture of synchronous and asynchronous iterative parallel algorithms of stationary or evolution variational inequations formulated by a multivalued model. The performances of synchronous and asynchronous iterative parallel methods are compared with previous ones obtained on cluster or when grid architecture is used. Thanks to the properties of the algebraic systems resulting from problem discretization we are able to analyze the behavior of the iterative algorithm in particular the convergence and the speed of convergence. The implementation of the studied methods on cloud architecture is described. Then we present various applications in particular the solidification of steel in continuous casting, the cavity pressure calculation described by a problem subject to unilateral constraints and finally a financial problem modeled by American option pricing.