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Moving Particle Semi-implicit (MPS) method and Smoothed Particle Hydrodynamics (SPH), as the meshfree particles methods,  have been widely applied in modeling free surface flows. However, application of the meshfree methods was still limited due to the problem of compressible stress instability, which usually occurs in presence of repulsive forces when particles are approaching to each other. The fundamental reason of the compressible stress instability is that the repulsive force first increases and then decreases as two particles get close in the compressible state, and the low accuracy of the numerical schemes for pressure gradient. In this paper, a new MPS-based numerical scheme is proposed to fundamentally improve the stability in the compressible state. Firstly, a modified quintic kernel function is adopted to guarantee the repulsive force always increases as two particles get close. Secondly, a symmetric form of the pressure gradient is employed based on the Taylor series expansion, which improves the accuracy of the gradient operator of the standard MPS method.