We present a calculation of the matrix elements of the most general set of Delta S = 2 dimension-six four-fermion operators. The values of the matrix elements are given in terms of the corresponding B-parameters. Out results can be used in many phenomenological applications, since the operators considered here give important contributions to K-0-(K) over bar(0) mixing in several extensions of the Standard Model (supersymmetry, left-right symmetric models, multi-Higgs models etc.). The determination of the matrix elements improves the accuracy of the phenomenological analyses intended to put bounds on basic parameters of the different models, as for example the pattern of the sfermion mass matrices. The calculation has been pet-formed on the lattice, using the tree-level improved Clover action at two different values of the strong coupling constant (beta = 6/g(0)(2)(a)= 6.0 and 6.2, corresponding to a(-1) = 2.1 and 2.7 GeV respectively), in the quenched approximation. The renormalization constants and mixing coefficients of the lattice operators have been obtained non-perturbatively.