Abstract: The band saw comprises two wheels spaced from each other and mounted for rotation on a support. A saw blade is trained under tension about the wheels, one of which is a power driven wheel. The bearing surfaces of both the wheels are provided with grooves which are closed upon themselves and run parallel to one another and to the rims of the wheels. The individual grooves on the one wheel are aligned with the respective opposite grooves on the other wheel in such a way that the planes running through the same are parallel to one another. The grooves, especially at least those two grooves lying opposite to each other on the one and the other wheel in the direction towards the teething of the saw blade and having the same width and the same depth, provide for an excellent bearing and guiding of the saw blade trained about the wheels. The saw blade need not to be aligned, stretched or levelled during the operation.