A B-spline box-based multi-channel method for treating Rydberg series is applied for systematic calculations of transition probabilities in neutral sulfur for energy levels up to n = 12. Extensive configuration-interaction wavefunctions in close-coupling form are used to represent the atomic levels. Special attention is paid to the treatment of inner-core and core-valence correlations at the same level of accuracy for all states. Non-orthogonal sets of one-electron radial functions are used to account for the strong term dependence of these orbitals. Relativistic effects are included through correction terms of the Breit-Pauli Hamiltonian. The agreement in the length and velocity gauges of the transition data and the accuracy of the binding energies are used to estimate the accuracy of our results, which are also compared with previous theoretical predictions, experimental measurements, and values predicted from astrophysical data.