The article discusses the contact interaction of deformable building constructions or their parts. Such interaction is realized for example at: hydraulic structures; suspension pile foundations, girder, raft, sheet piling; friction bearings and kinematic bearings of seismically insulated buildings, etc. The subject of the study is the formulation of the contact interaction problem as a linear complementarity problem. Such formulation of the problem allows the use of effective step-by-step algorithms and provides minimum qualification requirements to user. Expansion of existing formulations of the problems of frictionless contact and contact with the known friction bound in the form of linear complementarity problem to the formulation of the frictional contact is offered. Eventually, a heuristic formulation of the contact problem with friction is obtained in the form of a linear complementarity problem. The problem is solved by the Lemke step-type algorithm in the form of a displacement method. The results of the solutions obtained on test problems and on the Ansys software almost coincide with the results obtained by the proposed algorithm.