The aim of this work is to deduce the existence of solutionof a coupled problem arising in elastohydrodynamiclubrication. The lubricant pressure and concentration aremodelled by Reynolds equation, jointly with the free-boundaryElrod-Adams model in order to take into account cavitationphenomena. The bearing deformation is solution of Koitermodel for thin shells. The existence of solution to thevariational problem presents some difficulties: the coupledcharacter of the equations, the nonlinear multivaluedoperator associated to cavitation and the fact of writing theelastic and hydrodynamic equations on two different domains.In a first step, we regularize the Heaviside operator.Additional difficulty related to the differentdomains is circumvented by means of prolongation andrestriction operators, arriving to a regularized coupledproblem. This one is decoupled into elastic and hydrodynamicparts, and we prove the existence of a fixed point for theglobal operator. Estimations obtained for theregularized problem allow us to prove the existence ofsolution to the original one. Finally, a numerical method is proposed in orderto simulate a real journal-bearing device and illustrate the qualitative andquantitative properties of the solution.