A cutting tool has a tool body having at least one pocket, at least one cutting insert releasably fixed to the pocket and a fastening device for securing the insert in the pocket. The pocket has a raised portion) with a flat upper support face arranged to be received in a recess of the insert and support the insert by receiving a bottom surface of the recess bearing on the support face. A projecting member of the raised portion has delimiting walls designed to bear against border walls of the recess of an insert for establishing mutual contact therewith and prevent rotation of the insert in the pocket by receiving a rotational moment acting on the insert in an active chip-removing state of the tool.