Two important steps in the fabrication of microsphere laser fusion targets have been analyzed by simple mathematical modeling. Volatile‐containing droplets emerging from a nozzle with imposed oscillation first undergo a spontaneous blowing process, driven by the evaporation of volatile solvent which pushes the polymeric shell outward. These hollow particles then enter a refinement zone, where a centering process takes place to eliminate eccentricity between the shell internal and external surfaces. The confined vapor partially permeates to the surroundings, allowing shrinkage of the microspheres in this zone to the desired final dimensions and sphericity. Biaxial extensional flow dominates the rheology of micropshere expansion, whereas detailed dynamics of radial flow results in improved concentricity and sphericity. The effects of viscoelasticity on the rate and stress associated with microsphere expansion have been studied using the Newtonian and Maxwell constitutive equations. Simple analytic results to describe microsphere refinement have been obtained for conditions representative of the centering process where Newtonian behavior prevails as the fluid flow is relatively weak.