In this paper, the characteristics of incompressible flow in the linear piston pump for the solid transferring have been investigated. ACFX program has been used to obtain the solutions for the problems of three-dimensional, turbulent water flow in the linear piston pump. Based on the numerical analysis, a qualitative flow model for the linear piston pump is suggested. The velocity and the pressure distribution are obtained using the turbulent k-ε model. On the pump inside the water to fill the piston according to moving from the normal operation condition which is coming, the water led and the inlet valve flowed the discharge valve led and at the pump outside was discharged internal cylinder. TheSpeed of the piston which is satisfied the flow rate 500ℓ/min which considers from basic design became 0.16m/s. This paper could be applied to the design of the linear pistion pump for the fish transferring.