Due to its simplicity and low cost, laser speckle imaging (LSI) has achieved widespread use in biomedical applications. However, interpretation of the blood-flow maps remains ambiguous, as LSI enables only limited visualization of vasculature below scattering layers such as the epidermis and skull. Here, we describe a computational model that enables flexible study of the impact of these factors on LSI measurements. The model uses Monte Carlo methods to simulate light and momentum transport in a heterogeneous tissue geometry. The virtual detectors of the model track several important characteristics of light. This model enables study of LSI aspects that may be difficult or unwieldy to address in an experimental setting, and enables detailed study of the fundamental origins of speckle contrast modulation in tissue-specific geometries. We applied the model to an in-depth exploration of the spectral dependence of speckle contrast signal in the skin, the effects of epidermal melanin content on LSI, and the depth-dependent origins of our signal. We found that LSI of transmitted light allows for a more homogeneous integration of the signal from the entire bulk of the tissue, whereas epi-illumination measurements of contrast are limited to a fraction of the light penetration depth. We quantified the spectral depth dependence of our contrast signal in the skin, and did not observe a statistically significant effect of epidermal melanin on speckle contrast. Finally, we corroborated these simulated results with experimental LSI measurements of flow beneath a thin absorbing layer. The results of this study suggest the use of LSI in the clinic to monitor perfusion in patients with different skin types, or inhomogeneous epidermal melanin distributions.