Abstract Metamaterials have allowed unprecedented control of physical fields by harnessing material tensors derived from coordinate-transformation of governing equations. Among them, hydrodynamic metamaterials have recently received immense interests, showing the possibility of viscous flow control. However, the extant metamaterials cannot work for laminar flow which accompanies inertia force as well as viscous force. Herein, we propose a novel methodology for manipulating laminar flow to use the material tensors derived from the coordinate-transformed Navier–Stokes equations. The laminar flow manipulators for cloaking, concentrating, and rotating hydrodynamic flows are implemented numerically by applying both tensoric viscosity and density. The tensors give a direction for designing and fabricating metamaterials to control laminar flow.