Biofilms are communities of microbes that are bound to each other, and frequently to surfaces, by a matrix of polymers and proteins. As a result, biofilms have mechanical properties, of adhesion and cohesion, that are not present for the same types of microbes in their non-biofilm state. Recent work from our lab shows that forces resulting from adhesion are an important cue in initiating biofilm development (Rodesney et al., 2017 PNAS) and that cohesive forces between constituent microbes help biofilms resist clearance by the immune system (unpublished). I will present a brief sketch on both of these results and indicate how we anticipate that mathematical modeling could help guide the development of new types of approaches to combating biofilms. These approaches would target mechanical properties, of the environment and the biofilm, and therefore would be orthogonal to extant approaches to preventing and remediating biofilms. Standard molecular and genetic mechanisms for antibiotic resistance will not impinge on the mechanical anti-biofilm approaches we propose, which therefore will provide no selective pressure promoting the evolutionary development of antibiotic resistance.