Abstract: Since processed substrates usually exhibit nonplanar surface structures in Micro-Electro-Mechanical-Systems (MEMS) etching, a two-dimensional (2D) fluid model is developed to simulate the characteristics of the sheath near a conductive substrate with a circular trench, which is placed in an argon discharge powered by a radio-frequency (rf) current source. The model consists of 2D time-dependent fluid equations, the Poisson equation, and a current balance equation that can self-consistently determine the instantaneous voltage on the substrate placed on a powered electrode. The effects of both the aspect ratio (depth/width) and the structure of the trench on the characteristics of the sheath are simulated. The time-averaged potential and electric field in the sheath are calculated and compared for different discharge parameters. The results show that the radial sheath profile is not uniform and always tends to adapt to the contour of the substrate, which is believed to be the moulding effect. Affected by the structure of the substrate surface, the potential and electric field near the inner and outer sidewalls of the trench exhibit obvious non-uniformity, which will inevitably lead to non-uniformity in etching, such as notching. Furthermore, with a fixed amplitude of the rf current source, the potential drops and the sheath thickness decrease with an increase in aspect ratio.