The transport of sheet electron beam through the drift tube tunnel under uniform magnetic field has been analyzed. The edge curling due to the sharp increase of horizontal component of the space charge field has been explained by a windlike shear model, and an expression for vertical displacement of the beam edge from the top or bottom surface of the beam is derived on the basis of the aforementioned model. The effect of the height fill factor of the beam on the vertical displacement of the beam edge is analyzed analytically and then validated with numerical results by CST Particle Studio and OPERA 3-D software tools by considering some useful beam parameters. The vertical displacement of the beam edge enhances, and the higher portion of the beam is affected when it transports through short periodic vane-loaded interaction structures. For the sheet beam transport through planar vane-loaded structures suitable for subterahertz traveling-wave tube, the sum of the drift tube tunnel height and twice of the vane height should be considered as the effective tunnel height to calculate the required magnetic field in order to keep the vertical displacement maximum up to some desired value so that the beam edges must not strike on the vanes.