Abstract This study presents an idealized quantitative model of stress development and incremental fracturing in cooling lavas. It appears that columnar jointing forms in lavas by a process of incremental fracturing driven by thermal stresses. The fractures progress inward from the cooling surfaces as time increases. The cooling of a horizontal layer of lava has been modeled analytically for three cooling regimes: conductive cooling with liquid magma present, conductive cooling after total solidification, and hydrothermal cooling. Horizontal thermal stresses develop and cause vertical fractures at the upper and lower surfaces of the lava. As the lava cools, layer after layer becomes elastic. Thermal stresses develop in these thin layers, between previously fractured lava (where, it is assumed, stresses have been released), and the hot interior lava where temperatures exceed the elastic temperature limit. Stresses are analyzed by treating each unfractured elastic layer as a slab, restrained in bending, unrestrained from contraction. The stress level at which incremental fracturing occurs, extending previous fractures, and the effect of stress and temperature conditions on fracture penetration, are discussed. Our analysis yields values for the length of incremental fracture as a function of time and material strength for both a thin lava flow cooling conductively (incremental fracture lengths increase with time), and for a thicker lava flow in which hydrothermal convection is important (incremental fracture lengths are constant with time). Our results are compared to observed striae widths measured from the base of basaltic lava columns (striae represent successive incremental fractures). The comparison shows agreement in magnitude and trend after some amount of cooling i.e., striae and incremental fracture lengths increase with time at an accelerating rate.