A sole structure for an article of footwear comprising: a midsole (10, 110, 210, 510) that has a first side (17, 517) with a first surface (50, 550) and a second side (26, 526) with a second surface (52, 552); wherein the second side (26, 526) is opposite from the first side (17, 517); wherein the first side (17, 517) has a plurality of recesses (54, 154, 254, 554) extending toward the second side (26, 526) without extending to the second surface (52, 552); wherein the recesses (54, 154, 254, 554) are configured so that a thickness of the midsole between the second side and a deepest extent of each of the recesses is substantially uniform; wherein the midsole is a foam material that has a first density in a first portion along the first surface (50, 550) and a second density in a second portion adjacent the first portion; and wherein the second density is less than the first density, wherein the article of footwear has a heel region, a midfoot region, and a forefoot region; wherein the midsole has a heel portion, a midfoot portion, and a forefoot portion corresponding with the heel region, the midfoot region, and the forefoot region, respectively; wherein the recesses (54, 154, 254, 554) include a first set of recesses in the forefoot portion and a second set of recesses in the midfoot portion; wherein the recesses of the first set of recesses are spaced from one another to establish a first minimum wall thickness between adjacent ones of the recesses of the first set of recesses; wherein the recesses of the second set of recesses are spaced from one another to establish a second minimum wall thickness between adjacent ones of the recesses of the second set of recesses; and wherein the first minimum wall thickness is greater than the second minimum wall thickness. a midsole (10, 110, 210, 510) that has a first side (17, 517) with a first surface (50, 550) and a second side (26, 526) with a second surface (52, 552); wherein the second side (26, 526) is opposite from the first side (17, 517); wherein the first side (17, 517) has a plurality of recesses (54, 154, 254, 554) extending toward the second side (26, 526) without extending to the second surface (52, 552); wherein the recesses (54, 154, 254, 554) are configured so that a thickness of the midsole between the second side and a deepest extent of each of the recesses is substantially uniform; wherein the midsole is a foam material that has a first density in a first portion along the first surface (50, 550) and a second density in a second portion adjacent the first portion; and wherein the second density is less than the first density, wherein the article of footwear has a heel region, a midfoot region, and a forefoot region; wherein the midsole has a heel portion, a midfoot portion, and a forefoot portion corresponding with the heel region, the midfoot region, and the forefoot region, respectively; wherein the recesses (54, 154, 254, 554) include a first set of recesses in the forefoot portion and a second set of recesses in the midfoot portion; wherein the recesses of the first set of recesses are spaced from one another to establish a first minimum wall thickness between adjacent ones of the recesses of the first set of recesses; wherein the recesses of the second set of recesses are spaced from one another to establish a second minimum wall thickness between adjacent ones of the recesses of the second set of recesses; and wherein the first minimum wall thickness is greater than the second minimum wall thickness.