The lens–fibre interference (LFI) technique is used for monitoring thickness variations of a known refractive index transparent sheet. The sheet is inserted in the light path between the cylindrical lens and the fibre, in the LFI optical arrangement. A phase change and a geometrical shift for the beam passed through the sheet are observed. The presence of the sheet is considered in the ray tracing model which explained LFI (J. Opt. A: Pure Appl. Opt. 2:234–238, 2000). So, we are able to reproduce the interference pattern, in the presence of the sheet, theoretically. Depending on the width of the incident light spot on the cylindrical lens, a three beams interference could be observed. A development of the previous model is presented taking into account the third interfered beam. The produced interference pattern is a good indicator to the sheet’s thickness variations, especially when we considered the occurred three beams interference. Some investigations about the uncertainty analyses in our measurements are presented.