A study of the changes of molecular packing in self-assembled monolayers of alkylthiols on Au(111) induced by external pressure is presented. Atomic force microscopy (AFM) is used to apply pressure and to measure the height of islands of alkanethiols partially covering the gold surface. The islands are made of ordered straight chain alkylthiol molecules tilted from the surface normal. Their height was found to decrease in a stepwise manner as a function of the load applied by the tip. Simultaneous stepwise increases in friction force were observed. A simple geometrical model involving the interlocking of alkyl chains at specific molecular tilt angles can explain the observations. According to the model, tilts in both the nearest neighbor and the next-nearest neighbor directions are necessary.