Profiles of narrow and deep trenches produced by plasma ion etching have been simulated by a Monte Carlo method based on simple collision model. In the plasma etching process, ions from the bulk plasma are introduced into the sheath layer to be accelerated by the electric field toward the electrode plate. A substrate on the electrode plate is etched by the incident ions, whose kinetic energy and travelling direction are modified by random collisions with the neutrals in the sheath. We have simulated the ion etching process assuming an elastic collision between the ions and the neutrals in the sheath layer. Distribution functions for the ion energy and its arrival angel at the substrate surface have been obtained, and they have been used for computation of the time-dependent etch profile of the substrate by string algorithm. Profile of the etched trench has higher aspect ratio when the ratio between the mean free path of the ion and the thickness of the sheath layer(MFP/Sh) is larger. The etch rate decreases as the MFP/Sh ratio becomes smaller and the mask width narrower, which agrees with the experimental observations. The so-called "dove tail"(or "trenching") shape observed at the bottom corner of the etched trench may be simulated successfully by considering the ions glancing from the side wall after collision at low angles.