Polymer-containing solutions used across research and industry are commonly exposed to mechanically harsh fluid processes, for example shear and extensional forces during flow through porous media or rapid microdispensing of biopharmaceutical molecules. These forces are strong enough to break the covalent bonds in the polymer backbone. As this scission phenomenon can change the functional and fluid-flow properties as well as introduce reactive radicals into the solution, it must be understood and controlled. Experiments and models to date have only provided partial or qualitative insights into this behaviour. Here we build a link between the molecular-scale degradation models and the macroscale laminar flow of dilute solutions in any given geometry. A free-draining bead–rod model is used to investigate rupture events at the molecular scale. It is shown by uniaxial extension simulations of an ensemble of chains that scission can be conveniently described at the macroscopic scale as a first-order reaction whose rate is a function of the conformation tensor of the macromolecules and the velocity gradient of the flow. This approach is implemented in the finite volume code OpenFOAM by elaborating an appropriate constitutive equation for the conformation tensor. The macroscopic model is run and analysed for ultra-dilute solutions of poly(methyl methacrylate) in ethyl acetate and polyethylene oxide in water, using the geometry of an abrupt contraction flow and neglecting any viscoelastic effect. This multiscale approach bridges the gap between phenomenological observations of mechanically induced chemical degradation in large-scale applications and the rich field of molecular-scale models of macromolecules under flow.