We study experimentally the critical conditions for incipient motion of a single spherical particle deposited on a regular substrate under laminar flow conditions. The substrates are triangular and quadratic arrangements of identical glass spheres. For the latter configuration, the distance between the substrate spheres is varied, resulting in different partial shielding of the deposited particle to the shear flow. For the studied particle Reynolds numbers range between 3 × 10−4 and 3, the critical Shields number is independent from the particle density and from the particle Reynolds number but it depends significantly on the geometry of the substrate. Depending on the spacing between the substrate beads and thus on the exposure of the particle to the flow, we have observed an increase of about 50 percent in the critical Shields number. Studying the onset of particle motion as a function of the orientation of the substrate to the flow direction we find that the critical Shields number changes by up to a factor of 2, which is mainly due to the fact that the particle travels through the troughs of the substrate and hence the shear force in travel direction diminishes if not in line with the flow direction. Besides the critical Shields number we study the initial stage of particle motion by detecting the minimum time that is necessary for maintaining a certain Shields number to change the position of a single particle on the regular substrates. In the range studied, the initial stage of motion on the scale of the substrate's periodicity is mainly governed by the equilibrium particle motion.