A machine for treatment and/or analysis of biological samples, including a hinged arm to which a clamp for gripping a first biological sample holder is fixed. The clamp including first and second arms able to move relative to each other along a gripping position between a first position of gripping the first biological sample holder, and a first position of releasing the biological sample holder. Each arm of the clamp includes a groove. When the first and second arms are in the first position of release, the first and second grooves are spaced away from each other along the gripping direction, and when the first and second arms are in the first gripping position, the first and second grooves are brought closer to each other along the gripping direction, so as to be able to receive lateral edges of the first biological sample holder, so as to grip it by squeezing the lateral edges along the gripping direction.