To improve solutions for applications with complex boundary conditions and multimaterial/ multi-physics aspects, we apply a meshless method that alleviates the burden of grid generation and manipulation. We applied the Meshless Local Petrov-Galerkin (MLPG) method to demonstrate the advantages of using meshless numerical methods for multi-material interactions. The MLPG method uses a domain characterized by a field of nodes in which a local region influences the solution at each node. Node by node discretization of the governing equations and solution of the local weak formulation leads to a naturally coupled system of equations and the flexibility to properly handle multiple materials. To date, this method has been primarily applied to solid mechanics benchmark problems. The modeling of transient multi-fluid interfaces in multiple dimensions is necessary to solve meaningful problems. We have demonstrated that the MLPG method can solve such problems confirming its potential as an effective method for simulating complex multi-material/multiphysics systems.