A shoe sole structure includes a midsole body that extends from the heel region to the forefoot region of a shoe and an outsole that is attached to the midsole body. The outsole includes a plurality of protrusions arranged transversely to the longitudinal axis of the shoe, while extending at least partially between the lateral edge and the medial edge of the shoe. One or more of the half tube structures can include grooves and/or projections to enhance traction on a contact surface.