Abstract The members of many offshore structures and pipelines are circular cylinders which are often near to or penetrating the fluid boundaries, i.e. the sea bed, other solid boundary or free surface. It seems appropriate therefore to collect together some known analytical results concerning the cylinder added masses in such cases, the free surface ( z = 0 ) condition being simplified. Comparison with simple experiments indicates that for horizontal motions, ϖφ/ϖz = 0 z = 0 is appropriate while for vertical motions φ = 0 on z = 0 is appropriate. The effects caused by the variation in the added mass with cylinder submergence in both modes are important for a wide range of practical situations. For high speed entry (slamming) of the cylinder the effect of free surface rise is significant.