Significance Pattern formation is a central question in developmental biology. Alan Turing proposed that this could be achieved by a diffusion-driven instability in a monophasic system consisting of two reacting chemicals. In this paper, we extend Turing’s work to a more realistic mechanochemical model of multicellular tissue, modeling also its biphasic and mechanical properties. Overcoming limitations of conventional reaction–diffusion models, we show that mechanochemical couplings between morphogen concentrations and extracellular fluid flows provide alternative, non-Turing, mechanisms by which tissues can form robust spatial patterns.