Multi-axis differential optical absorption spectroscopy (MAX-DOAS) is a widely used measurement technique for the detection of a variety of atmospheric trace gases. Using inverse modelling, the observation of trace gas column densities along different lines of sight enables the retrieval of aerosol and trace gas vertical profiles in the atmospheric boundary layer using appropriate retrieval algorithms. In this study, the ability of eight profile retrieval algorithms to reconstruct vertical profiles is assessed on the basis of synthetic measurements. Five of the algorithms are based on the optimal estimation method, two on parametrised approaches, and one using an analytical approach without involving any radiative transfer modelling. The synthetic measurements consist of the median of simulated slant column densities of O4 at 360 and 477 nm, as well as of HCHO at 343 nm and NO2 at 477 nm, from seven datasets simulated by five different radiative transfer models. Simulations are performed for a combination of 10 trace gas and 11 aerosol profiles, as well as 11 elevation angles, three solar zenith, and three relative azimuth angles. Overall, the results from the different algorithms show moderate to good performance for the retrieval of vertical profiles, surface concentrations, and total columns. Except for some outliers, the root-mean-square difference between the true and retrieved state ranges between (0.05–0.1) km−1 for aerosol extinction and (2.5–5.0) ×1010 molec cm−3 for HCHO and NO2 concentrations.