A clamping apparatus for a saddle of a bicycle having a seat post with two side faces, and characterized in that the clamping apparatus comprises: two clamping mounts being adapted to respectively abut the side faces of the seat post, and each clamping mount having: a top; a bottom; an outer side; a top face formed curved on and protruding downwardly from the outer side of the clamping mount at the top of the clamping mount to form a holding recess; two elongated through holes formed through the outer side of the clamping mount at an interval; and a clamping block formed on and protruding from the outer side of the clamping mount at the bottom of the clamping mount between the elongated through holes and having: a top; and an abutment face formed aslant on and protruding from the top of the clamping block; two clamping elements respectively and detachably mounted in the clamping mounts between the holding recesses and the clamping blocks, and each clamping element having: a top; a bottom; a middle; a top clamping recess formed in the top of the clamping element and selectively facing the holding recesses of a corresponding clamping mount; a bottom clamping recess formed in the bottom of the clamping element and selectively facing the holding recesses of the corresponding clamping mount; a top abutting recess formed aslant through the middle of the clamping element at the top of the clamping element, communicating with the top clamping recess and selectively abutting against the clamping block of the corresponding clamping mount and having a depth; and a bottom abutting recess formed aslant through the middle of the clamping element at the bottom of the clamping element, communicating with the bottom clamping recess and selectively abutting against the clamping block of the corresponding clamping mount and having a depth being deeper than the depth of the top abutting recess; and two fasteners respectively connected to the clamping elements and the clamping mounts to connect the clamping elements and the clamping mounts with the seat post to clamp the saddle. two clamping mounts being adapted to respectively abut the side faces of the seat post, and each clamping mount having: a top; a bottom; an outer side; a top face formed curved on and protruding downwardly from the outer side of the clamping mount at the top of the clamping mount to form a holding recess; two elongated through holes formed through the outer side of the clamping mount at an interval; and a clamping block formed on and protruding from the outer side of the clamping mount at the bottom of the clamping mount between the elongated through holes and having: a top; and an abutment face formed aslant on and protruding from the top of the clamping block; a top; a bottom; an outer side; a top face formed curved on and protruding downwardly from the outer side of the clamping mount at the top of the clamping mount to form a holding recess; two elongated through holes formed through the outer side of the clamping mount at an interval; and a clamping block formed on and protruding from the outer side of the clamping mount at the bottom of the clamping mount between the elongated through holes and having: a top; and an abutment face formed aslant on and protruding from the top of the clamping block; a top; and an abutment face formed aslant on and protruding from the top of the clamping block; two clamping elements respectively and detachably mounted in the clamping mounts between the holding recesses and the clamping blocks, and each clamping element having: a top; a bottom; a middle; a top clamping recess formed in the top of the clamping element and selectively facing the holding recesses of a corresponding clamping mount; a bottom clamping recess formed in the bottom of the clamping element and selectively facing the holding recesses of the corresponding clamping mount; a top abutting recess formed aslant through the middle of the clamping element at the top of the clamping element, communicating with the top clamping recess and selectively abutting against the clamping block of the corresponding clamping mount and having a depth; and a bottom abutting recess formed aslant through the middle of the clamping element at the bottom of the clamping element, communicating with the bottom clamping recess and selectively abutting against the clamping block of the corresponding clamping mount and having a depth being deeper than the depth of the top abutting recess; and a top; a bottom; a middle; a top clamping recess formed in the top of the clamping element and selectively facing the holding recesses of a corresponding clamping mount; a bottom clamping recess formed in the bottom of the clamping element and selectively facing the holding recesses of the corresponding clamping mount; a top abutting recess formed aslant through the middle of the clamping element at the top of the clamping element, communicating with the top clamping recess and selectively abutting against the clamping block of the corresponding clamping mount and having a depth; and a bottom abutting recess formed aslant through the middle of the clamping element at the bottom of the clamping element, communicating with the bottom clamping recess and selectively abutting against the clamping block of the corresponding clamping mount and having a depth being deeper than the depth of the top abutting recess; and two fasteners respectively connected to the clamping elements and the clamping mounts to connect the clamping elements and the clamping mounts with the seat post to clamp the saddle.