Morphogenesis in living organisms relies on the integration of both biochemical and mechanical signals. During the last decade, attention has been mainly focused on the role of biochemical signals in patterning and morphogenesis, leaving the contribution of mechanics largely unexplored. Fortunately, the development of new tools and approaches has made it possible to re-examine these processes. In plants, shape is defined by two local variables: growth rate and growth direction. At the level of the cell, these variables depend on both the cell wall and turgor pressure. Multidisciplinary approaches have been used to understand how these cellular processes are integrated in the growing tissues. These include quantitative live imaging to measure growth rate and direction in tissues with cellular resolution. In parallel, stress patterns have been artificially modified and their impact on strain and cell behavior been analysed. Importantly, computational models based on analogies with continuum mechanics systems have been useful in interpreting the results. In this review, we will discuss these issues focusing on the shoot apical meristem, a population of stem cells that is responsible for the initiation of the aerial organs of the plant.