Recent reports show that, after nuclear envelope breakdown, lamin-B, a component of the nuclear lamina in interphase, localizes around the mitotic spindle as a membranous network. How this process occurs, however, and how it influences mitotic spindle morphogenesis is unclear. Here, we develop a computational model based on a continuum description to represent the abundance and location of various molecular species involved during mitosis, and use the model to test a number of hypotheses regarding the formation of the mitotic matrix. Our model illustrates that freely diffusible nuclear proteins can be captured and transported to the spindle poles by minus-end-directed microtubule (MT) motors. Moreover, simulations show that these proteins can be used to build a shell-like region that envelopes the mitotic spindle, which helps to improve the focusing of the mitotic spindle by spatially restricting MT polymerization and limiting the effective diffusion of the free MTs. Simulations also confirm that spatially dependent regulation of the spindle network through the Ran system improves spindle focusing and morphology. Our results agree with experimental observations that lamin-B reorganizes around the spindle and helps to maintain spindle morphology.