Distribution systems infrastructure is exposed continuously to a range of high-impact low-probability (HILP) events, such as natural hazards. Due to the increased frequency of these extreme events, the resilience of the power distribution system (PDS) is becoming critical. In this paper, a novel methodology is proposed for the optimal planning of distributed generation (DG) to enhance the resilience of PDS against the impact of lahars, which can occur following a volcanic eruption. The concept of vulnerability curves is introduced to determine the unavailability of the elements system. The proposed methodology includes a stochastic optimization problem (SOP) and Monte Carlo simulation method (MCS) to consider two uncertainties levels: the speed and density of lahars. Our proposal is applied to the IEEE 37-node test feeder. The results demonstrate that the average energy not supplied (ENS) during the restoration time obtained from the simulated scenarios is 1.37 MWh for the actual PDS and 1.02 MWh when optimal planning of DG is applied.