This study presents Navier-Stokes incompressible hydrodynamic for simulation modelling of steady current around offshore pipelines on horizontal 2D. The model is simulated in the vicinity of a pipe with 0.1 meter in diameter. RANS (Reynolds-Averaged Navier-Stokes) is used to solve the current flow field; hence the seabed under the pipeline is classified as a smooth and no-slip condition is applied where friction is neglected above the pipe surface. The analytical is based on numeric solution, current flow field, vortex shedding and shear stress distribution concerning the existing pipe.