A constitutive equation for concentrated suspensions in Newtonian liquids is derived, based on an empirical form of the motion of the suspended particles, and the lubrication forces between them. The key idea in the model is that the assumed relative motion between two generic particles consists of an affine motion, plus a fluctuation, with a strength proportional to the strain rate. Other well‐founded empiricisms, including Hinch and Leal’s closure assumption and Krieger’s viscosity form, are adopted to produce a useful constitutive equation. The constitutive equation has several attractive features, including an instantaneous and linear response in the strain rate, a relaxation in the start up flow, a full recovery in the restart of the flow in the same direction, a partial recovery in the restart of the flow in the opposite direction, and a universal response in the strain in transient flows. An evaluation of the model in some simple homogeneous flows is made.