At low temperature, T -> 0, the yield stress of a perfect crystal is equal to its so called theoretical strength. The yield stress of non-perfect crystals is controlled by the stress threshold of dislocation mobility. A non-crystalline solid has neither an ideal structure nor gliding dislocations. Its yield stress, i.e. the stress at which the macroscopic inelastic deformation starts, depends on distribution of local, attributed to each atomic site, critical stresses at which the local inelastic deformation occurs. We describe exactly solvable model of planar layer strength and sliding with an arbitrary homogeneous distribution of local critical stresses. The macroscopic stress threshold of the athermal sliding is found. Kinetics of thermally-activated creep of the sliding layer is described. The rate of the thermally activated sliding is tightly connected with parameters of the low temperature strength. The sliding activation volume scales with the applied external stress as ~ \sigma ^-\beta, where \beta <1. The proposed model accounts for mechanisms and the yield stress of the low temperature deformation of polycluster metallic glasses, since intercluster boundaries of a polycluster metallic glass are natural sliding layers of the described type.