We describe the WA89 Collaboration experimental data on Lambda, Sigma(-), Sigma(+), Xi(-), and Omega(-) baryons, and bar(Lambda) and bar(Xi(+)) antibaryons production in Sigma(-) collisions with C and Cu targets at 345 GeV/c (sqrt(s_(Sigma N)) ~ 25.5 GeV) in the frame of the Quark-Gluon String Model. How the theoretical results compare to the experimental data is discussed. Finally, some relations among the values of the model parameters obtained with the help of quark combinatorics are presented.