A mathematical model has been presented for a high speed liquid jet penetration into soft solid by a needle-free injection system. The model consists of a cylindrical column formed by the initial jet penetration and an expansion sphere due to continuous deposition of the liquid. By solving the equations of energy conservation and volume conservation, the penetration depth and the radius of the expansion sphere can be predicted. As an example, the calculation results were presented for a typical needle-free injection system into which a silicon rubber was injected into. The calculation results were compared with the experimental results.
