Stratospheric aerosols play an important role in the climate system by affecting the Earth's radiative budget as well as atmospheric chemistry, and the capabilities to simulate them interactively within global models are continuously improving. It is important to represent accurately both aerosol microphysical and atmospheric dynamical processes because together they affect the size distribution and the residence time of the aerosol particles in the stratosphere. The newly developed LMDZ-S3A model presented in this article uses a sectional approach for sulfate particles in the stratosphere and includes the relevant microphysical processes. It allows full interaction between aerosol radiative effects (e.g. radiative heating) and atmospheric dynamics, including e.g. an internally generated quasi-biennial oscillation (QBO) in the stratosphere. Sulfur chemistry is semi-prescribed via climatological lifetimes. LMDZ-S3A reasonably reproduces aerosol observations in periods of low (background) and high (volcanic) stratospheric sulfate loading, but tends to overestimate the number of small particles and to underestimate the number of large particles. Thus, it may serve as a tool to study the climate impacts of volcanic eruptions, as well as the deliberate anthropogenic injection of aerosols into the stratosphere, which has been proposed as a method of geoengineering to abate global warming.