We present extensive multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations including 106 states in doubly ionized silicon (Si III) and 45 states in triply ionized silicon (Si IV), which are important for astrophysical determination of plasma properties in different objects. These calculations represents an important extension and improvement of earlier calculations especially for Si III. The calculations are in good agreement with available experiments for excitation energies, transition properties, and lifetimes. Important deviations from the NIST-database for a selection of perturbed Rydberg series are discussed in detail.