Nonequilibrium Brownian dynamics simulations (NEED) are used to model the dynamics of semiflexible macromolecules undergoing shear how. The mathematical model utilizes a discretized version of the Kratky-Porod wormlike (or persistent) chain as the building block, generalized to include how. The Fokker-Planck equation resulting from such an analysis is converted to a stochastic differential equation from which the simulation algorithm for the NEED is obtained. Various conformational and rheological quantities are monitored, under both steady-state and transient conditions, with the primary independent variable being the flexibility parameter beta, the bending constant of the chain. The model qualitatively describes many of the experimentally observed effects in such systems, most notably birefringence overshoots, cessation effects, and various steady-state effects. In addition, many of the qualitative rheological features of both rigid rod (or flexible) polymers are captured as beta is made very large (or small). The advantage of the NEED over an analytical treatment is its ability to incorporate (analytically intractable) effects such as hydrodynamic interactions and its (natural) ability to obtain transient information, a facet useful in comprehending the differing dynamics of rigid and less rigid macromolecules.