Phylogenetic analyses based on models of molecular sequence evolution have driven to industrial scale the generation, cataloguing and modelling of nucleic acid and polypeptide structure. The recent application of these techniques to study the evolution of protein interaction networks extends this analytical rigour to the study of nucleic acid and protein function. Can we further extend phylogenetic analysis of protein networks to the study of tissue structure and function? If the study of tissue phylogeny is to join up with mainstream efforts in the molecular evolution domain, the continuum field description of tissue biophysics must be linked to discrete descriptions of molecular biochemistry. In support of this goal we discuss tissue units, and biophysical constraints to molecular function associated with these units, to present a rationale with which to model tissue evolution. Our rationale combines a multiscale hierarchy of functional tissue units (FTUs) with the corresponding application of physical laws to describe molecular interaction networks and flow processes over continuum fields within these units. Non-dimensional numbers, derived from the equations governing biophysical processes in FTUs, are proposed as metrics for comparative studies across individuals, species or evolutionary time. We also outline the challenges inherent to the systematic cataloguing and phylogenetic analysis of tissue features relevant to the maintenance and regulation of molecular interaction networks. These features are key to understanding the core biophysical constraints on tissue evolution.