We develop and extend the dynamical string parton model. This model, which is based on the salient features of QCD, uses classical Nambu-Gotō strings with the endpoints identified as partons, an invariant string breaking model of the hadronization process, and interactions described as quark-quark interactions. In this work, the original model is extended to include a phenomenological quantization of the mass of the strings, an analytical technique for treating the incident nucleons as a distribution of string configurations determined by the experimentally measured structure function, the inclusion of the gluonic content of the nucleon through the introduction of purely gluonic strings, and the use of a hard parton-parton interaction taken from perturbative QCD combined with a phenomenological soft interaction. The limited number of parameters in the model are adjusted to e + e − and p -p data. Utilizing these parameters, the first calculations of the model for p -A and A-A collisions are presented and found to be in reasonable agreement with a broad set of data. 25.75.+r, 12.38.Mh