Strengthening by needle-shaped β′′ precipitates is critical in Al–Mg–Si alloys. Here, the strengthening is studied computationally at the peak-aged condition where precipitate shearing and Orowan looping are usually considered to have equal strengths. Pseudo-random precipitate microstructures are constructed based on experimental precipitate dimensions and volume fractions at peak aging. A Discrete Dislocation Dynamics method is then adapted to compute the Critical Resolved Shear Stress (CRSS) for Orowan looping of dislocations moving through the non-shearable precipitate field. The CRSS for Orowan looping is determined by a typical in-situ precipitate spacing that is smaller than the average spacing and by the dislocation core energy within a radius of ≈5b, a factor rarely considered. The matrix misfit stresses, volume fraction, and precipitate shape have small effects on the CRSS. With microstructure and property details introduced as faithfully as possible, the CRSS for Orowan looping using atomistically-calibrated core energies at room temperature is nonetheless ≈33% higher than experiments. This suggests that precipitate shearing controls strength, and analyses of (i) forces acting on the precipitates, (ii) misfit stresses inside the precipitates, (iii) first-principles results for the relevant precipitate fault energies, and (iv) simulations that mimic precipitate shearing indicate a shearing CRSS closer to experiments. Thus, Orowan looping only sets an upper bound for the CRSS even at peak aging, and further quantitative progress requires detailed modeling of precipitate shearing.