This study deals with the formulation, mathematical property and phydival meaning of the simplified Navier-Stokes (SNS) eguations. The tensorial SNS equations proposed is the simplest in, form and is applicable to flow tields with arbitrary body boundaries. The zones of influence and dependence of the SNS equations, which are of primary importance to numerical solutions, are expounded for the first rime from the viewpoint of subcharacteristics. Besides, a detailed snalysis of the diffusion process in flow fields shows that the diffnsion effect has an influence zone globalty windward and an upwind propagation greatly depressed by, convection. The maximum upwind influential distance of the viscous effect and the relative importance of the viscous effect in the flow direction to that in the direction normal to the flow are represented by the Reynolds number, which illustrates the conversion of the complete Navier-Stokes (MS) equarions to the SNS equations for flows with large Reynolds numher.