Spectroscopic techniques involving flow-oriented samples and polarised light, such as linear dichroism (LD), are becoming increasingly useful to probe biomacromolecular assemblies. However, the magnitude of the signal and in some cases the shape of the spectrum are dependent on the distribution of the orientations of the molecules in the sample. Despite great progress in the modelling of dilute and semi-dilute suspension mechanics, these theories have had remarkably little impact on the community practising LD. We perform calculations with a model combining Brownian effects and rotations in a steady shear flow of a dilute suspension of rigid, rodlike particles. We calculate the time-dependent probability density functions for the orientation distributions of three biomolecular assemblies: M13 bacteriophage, DNA molecules of well-defined length, and FtsZ protofilaments. Our calculations allow us to compute directly (rather than infer from experiment) the LD orientation parameter, S, for such assemblies. The results from the model are consistent with experiment for M13 bacteriophage and allow us to estimate S empirically for reasonably short DNA molecules. In analysing the particle size distribution for the process of FtsZ polymerisation, we find that results from the model aid our understanding of the process.