Explicit finite difference (FD) schemes can realize highly realistic physical models of musical instruments but are computationally complex. A design methodology is presented for the creation of field-programmable gate array (FPGA)-based micro-architectures for FD schemes which can be applied to a range of applications with varying computational requirements, excitation and output patterns and boundary conditions. It has been applied to membrane and plate-based sound producing models, resulting in faster than real-time performance on a Xilinx XC2VP50 device which is 10 to 35 times faster than general purpose and digital signal processors. The models have developed in such a way to allow a wide range of interaction (by a musician) thereby leading to the possibility of creating a highly realistic digital musical instrument.