A mathematical model was developed to study shape evolution of trenches during plasma-assisted etching. A two- region sheath model was used to determine the effect of local potential distribution on ion deflection and on the ion flux and energy distribution along the walls of the trench. The potential field in the near-trench region was found by using the boundary integral method which, coupled with a moving boundary scheme, allowed the time evolution of etch profiles to be computed. The effect of important variables affecting ion deflection and sidewall etching was combined in a dimen- sionless group f~. For values ofO <~ 0.1 and for positive mask potentials, less than 10% of the bombarding ion flux struck the sidewall of a rectangular trench. Ion deflection and ion-neutral collisions resulted in sidewall "bowing" and in decreas- ing etch rate as a function of trench depth. Such phenomena are especially important in applications which require the etching of deep trenches. Attainment of anisotropy is an important driving force behind implementation of plasma-assisted etching tech- niques in semiconductor processing. Anisotropy is pro- rooted when ions gain directionality from the plasma sheath electric field and are accelerated toward the etch feature, thus enhancing the vertical etch rate by preferen- tial bombardment of the bottom surface. We call this "ion- assisted etching." On the other hand, isotropic etching, which leads to undercutting, is commonly associated with the presence of neutral etchant species which, lacking di- rectionality in motion, etch both the sidewalls as well as the bottom of the feature. We call this "chemical etching." The degree of etch anisotropy is thus often said to depend upon the relative importance of i0n-assisted etching as compared to chemical etching. However, sidewall etching can occur even in the absence