An outstanding challenge in modeling the radiative properties of stratiform rain systems is an accurate representation of the mixed-phase hydrometeors present in the melting layer. The use of ice spheres coated with meltwater or mixed-dielectric spheroids have been used as rough approximations, but more realistic shapes are needed to improve the accuracy of the models. Recently, realistically structured synthetic snowflakes have been computationally generated, with radiative properties that were shown to be consistent with coincident airborne radar and microwave radiometer observations. However, melting such finely-structured ice hydrometeors is a challenging problem, and most of the previous efforts have employed heuristic approaches. In the current work, physical laws governing the melting process are applied to the melting of synthetic snowflakes using a meshless-Lagrangian computational approach henceforth referred to as the Snow Meshless Lagrangian Technique (SnowMeLT). SnowMeLT is capable of scaling across large computing clusters, and a collection of synthetic aggregate snowflakes from NASA’s OpenSSP database with diameters ranging from 2–10.5 mm are melted as a demonstration of the method. To properly capture the flow of meltwater, the simulations are carried out at relatively high resolution (15 μm), and a new analytic approximation is developed to simulate heat transfer from the environment without the need to simulate the atmosphere explicitly.