When it moves through a yield stress fluid, a solid object continuously reaches and liquefies new solid regions, so that both flow in liquid regions and deformations in solid regions occur. In the present work, we focus on the displacement of a plate through simple yield stress fluids (nonthixotropic). Through force vs velocity and particle imaging velocimetry measurements with a detailed analysis of the deformation history, we are able to identify the solid and liquid regions and their respective role in the flow characteristics. It is shown that the displacement of a long object through a yield stress fluid gives rise to the formation of a liquid boundary layer (BL) of uniform thickness at short distance from the leading edge, while the rest of the material remains solid. The original result is that the thickness of this boundary layer, which is of the order of 10mm, only slightly increases with velocity and does not tend to zero when the velocity tends to zero, in contrast with usual flows of yield stress fluids along solid surfaces. Moreover, it does not change for significant variations of the rheological characteristics of the fluid in its liquid regime. We show that these specific characteristics of the liquid layer are mainly governed by the progressive transition from an elastic solid to a liquid, starting slightly ahead of the leading edge of the plate. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4720387]