A shoe sole having at least one midsole or outer surface portion that is concavely rounded relative to a space inside the shoe adapted to receive an intended wearer's foot. The sole includes a midsole and an outer sole. The midsole extends up the side of the sole to a vertical height above the vertical height of a lowest point of the inner midsole surface. The midsole includes a portion of greatest thickness in a side portion that is greater than a thickness of a second midsole portion located in a middle sole portion of the shoe sole. The combination of the midsole height and thickness with the concavely rounded surface portion together provide improved stability of the shoe sole.