cross sections alternatively grooves 30 and 40 may have a circular arc or triangular cross section still further grooves 30 and 40 may be a plurality of separated grooves arranged equiangularly on each sliding surface region 19a and 20 of swash plate 6 the radial width a of grooves 30 and 40 is preferably less than a third of the diameter l of shoes 8 the depth b of grooves 30 and 40 is preferably less than about 2 mm if the radial width a of grooves 30 and 40 significantly exceeds about 2 mm the engaging area between circular flat surface 8b of shoes 8 and the sliding surface region 19a and 20a becomes too small consequently circular flat surface 8b of shoes 8 becomes subjected to large reaction forces from pistons 5 on the other hand if radial width a of grooves 30 and 40 are too small grooves 30 and 40 fail to capture enough of the lubricating oil contained in the refrigerant gas alternatively the first preferred embodiment may have grooves 30 and 40 defining half circles corresponding to the bottom dead center of pistons 5 the arrangement accounts for the fact that shoes 8 thrust toward swash plate 6 in response to the reaction force of pistons 5 during the compression stage in the first preferred embodiment oil in the refrigerant gas fills grooves 30 and 40 during normal operation of the compressor and also is captured in grooves 30 and 40 upon initially starting of the compressor as a result local abrasion between swash plate 6 and shoes.