Accurate preliminary sizing of an aircraft is an essential input for its conceptual design and budgeting procedure. This paper introduces a preliminary sizing method for unmanned aerial vehicles (UAV), which can improve the accuracy of the traditional preliminary sizing methods. The mass estimation relationships (MERs) for three different UAV classes using the bending moment as an independent variable are developed based on the constrained quadratic regression. Analyses of the mass characteristics of the UAV classes identify the parameters used for the MERs. A new sizing procedure for a heavy (Class III) high/medium-altitude-long-endurance UAV using the developed weight relationship is proposed. A case study demonstrates the validity of the proposed procedure.