We consider contributions of R-parity-conserving softly broken supersymmetry (SUSY) to neutrinoless double beta (O nu beta beta) decay via the (B-L)-violating sneutrino mass term. The latter is a generic ingredient of any weak-scale SUSY model with Majorana neutrino mass. The new R-parity-conserving SUSY contributions to O nu beta beta are realized at the level of box diagrams. We derive the effective Lagrangian describing the SUSY-box mechanism of O nu beta beta decay and the corresponding nuclear matrix elements. The one loop sneutrino contribution to the Majorana neutrino mass is also derived. Given the data on the O nu beta beta decay half-life of Ge-76 and the neutrino mass we obtain constraints on the (B-L)-violating sneutrino mass. These constraints leave room for accelerator searches for certain manifestations of the second and third generation (B-L)-violating sneutrino mass term, but are most probably too tight for first generation (B-L)-violating sneutrino masses to be searched for directly.