In recent years, a number of research efforts have been devoted to understand the mechanisms and develop accurate simulation models for laser ablation of solid materials. However, uncertainty quantification (UQ) for laser ablation of solid materials, when the sources of uncertainty are inherently stochastic (e.g., material and optical properties of target materials at elevated temperatures), is not sufficiently understood or addressed, despite having critical impact on guiding experimental efforts and advanced manufacturing. In this paper, we consider the problem of UQ for pulsed laser ablation of aluminum. In particular, a generalized polynomial chaos (PC) method is used to incorporate constitutive parameter uncertainties within the representation of laser heat conduction phenomena, where the parameter uncertainties are either presumed from the mathematical modeling approximation for the laser heat conduction model and/or from the laser source. Moreover, numerical simulation studies for laser ablation of aluminum, with nanosecond Nd:YAG 266nm pulsed laser, that demonstrate the proposed generalized PC predictions are also presented. Finally, a sensitivity study is used to identify those parameters that provide the most variance in the thermal and ablation response.