In improved equipment for lapping internal surfaces, use is made of a composite lap (12), the rod (2) of which is held by the tool spindle (11) and inserted with a marginal degree of clearance into a cone (3) that carries the abrasive shell (4), and a chucking mechanism (1) located beneath and coaxial with the spindle and lap; errors are avoided, particularly with small-bore work, by embodying the lap rod (2) in three rigidly associated sections (7, 8 and 9), namely, a polygonal tip (7), insertable and fastened with a transverse pin (10) in a matching polygonal socket (13) offered by the cone (3), a flexible coupling section (8), and a shank (9) uppermost that is screwed into or otherwise clamped to the spindle. Work to be lapped is held in a chuck (1) suspended from at least three cables (5, 6) threaded through relative peripheral mountings (14) afforded by the chuck itself.