Both chemical and mechanical fields are known to play a major role in morphogenesis. In plants, the phytohormone auxin and its directional transport are essential for the formation of robust patterns of organs, such as flowers or leaves, known as phyllotactic patterns. The transport of auxin was recently shown to be affected by mechanical signals, and conversely, auxin accumulation in incipient organs affects the mechanical properties of the cells. The precise interaction between mechanical fields and auxin transport, however, is poorly understood. In particular, it is unknown whether transport is sensitive to the strain or to the stress exerted on a given cell. Here, we investigate the nature of this coupling with the help of theoretical models. Namely, we introduce the effects of either mechanical stress or mechanical strain in a model of auxin transport and compare the patterns predicted with available experimental results, in which the tissue is perturbed by ablations, chemical treatments, or genetic manipulations. We also study the robustness of the patterning mechanism to noise and investigate the effect of a shock that changes abruptly its parameters. Although the model predictions with the two different feedbacks are often indistinguishable, the strain feedback seems to better agree with some of the experiments. The computational modeling approach used here, which enables us to distinguish between several possible mechanical feedbacks, offers promising perspectives to elucidate the role of mechanics in tissue development, and may help providing insight into the underlying molecular mechanisms.