The combustion of a liquid fuel within a highly porous inert medium (PIM) has been investigated numerically and experimentally. A one-dimensional laminar flow model is used in this work. Combustion is modeled using a multistep reaction mechanism. Non-local thermal equilibrium between the gas, the liquid, and the solid phases is accounted for by considering separate energy equations for the three phases. Nongray solid radiation and droplet radiation absorption are included in the model. The equations for the liquid phase are formulated using a Lagrangian description and the equations for the gas and solid phases are formulated using an Eulerian description. A burner that allows effective control of the equivalence ratio and the burning rate is built to study the phenomena. Burning rates, temperature, and emissions are measured. Numerical results are obtained for droplet size and temperature history as well as flame speed and temperature profile within the burner. Effects of various parameters on the burner performance are studied. Predictions of the flame speed, the peak temperatures, and emissions are compared with experiments.