The Leslie-Ericksen continuum theory is used to study the steady-state isothermal and non-isothermal plane Poiseuille flow of a liquid crystalline material with the mean molecular orientation confined to the plane of shear. In the non-isothermal case a temperature difference is assumed across the channel height, which causes the flow to become intrinsically non-symmetric with respect to the centre plane of the channel. But, also for the isothermal Poiseuille flow, which is intrinsically symmetric with respect to the centre of the channel, non-symmetric solutions of the flow equations are found. In this first part the in-plane director, velocity and temperature profile of a flow-aligning nematic are investigated.