An analytical and numerical study of vaporization and combustion of an isolated liquid hydrocarbon droplet containing a single metal particle in its core is presented. The objective is to formulate a simplified vaporization model that can be used in spray combustion calculations. Further, the model is extended to include the combustion of the liquid fuel, so that ignition characteristics of the metal particle can be studied. The gas phase includes the effects of variable thermophysical properties and nonunitary Lewis number. The liquid phase includes the effects of transient heating and circulation. Results are presented for both a spherically symmetric configuration, and an axisymmetric case, where the liquid motion is analytically given. Calculations are made for both liquid vaporization without combustion and vaporization followed by combustion. The effects associated with varying solid loading are studied. The vaporization rates for a composite droplet are found to be close to those for a corresponding all-liquid droplet. Ignition times for the metal particle are found to depend on the solid mass loading, and can be several times larger than the liquid fuel burnout time. The heat transfer to the particle is convection dominated.