Polygonal fractures commonly form in basaltic lava flows during cooling of the molten lava. A transient thermomechanical model is constructed to apply the temperature history in a cooling basalt flow as a boundary condition in a mechanical model of viscoelastic stress in cooling basalt. Nearly all past modeling of stress in cooling basalt has treated the material as purely elastic below a well-defined glass transition temperature. An important distinction of this model is that the viscosity of the material is allowed to be temperature-dependent, and the effects of viscoelastic relaxation are included. On the basis of this research, faster cooling and higher strain rates lead to markedly higher effective glass transition temperatures, consistent with previous observations by researchers. The total thermal strain in the system is constant, yet the percentage of strain that is not relaxed by viscous flow varies with position relative to the cooling surface. This elastic strain partition is the portion of the total strain that creates stress in the material, and it is directly dependent on cooling rate. Thus a genetic link between cooling rate and magnitude of stress is identified. ¿ 2000 American Geophysical Union