Return collectors are predominant organs for rubber-tyred subways to operatesince they ensure both the track circuit shunt and the traction current return. Po- sitioned at the interface between the track and the rolling stock, they are subjected to the disruptions linked to the train movement and the track irregularities. One of the most critical steps is the crossing of a switch nose.This study aims at determining the collector position during this crossing by means of a quasi-static analysis of the system. Two approaches are investigated. The first one brings into play a rigid contact and geometrical angles. It enables to model the crossing until the contact with the crossing nose. The diving capability of the collector is also taken into account. The second one is a standard  approach of the contact. A slight penetration is considered, which allows to grasp the contact with  the crossing nose. The second advantage  is to prepare the ground for a complete dynamical analysis. Both approaches are then implemented on Matlab to solve the equations. Finally the study of the switch crossing in nominal conditionsand a parametric analysis are achieved for a specified switch.