A steering column support apparatus, comprising: a non-dropping bracket that is fastened to and supported by a vehicle body and located on the upper part of a middle section in the axial direction of a steering column, and that comprises a top plate that is provided in the axial direction of the steering column, and a pair of long holes formed in part of the top plate such that the long holes are parallel to each other, and extend in the axial direction of the steering column; a dropping bracket that is supported by the middle section in the axial direction of the steering column, and that comprises a bottom plate whose top surface faces the bottom surface of the top plate of the non-dropping bracket, and a pair of installation holes that are formed in part of the bottom plate in locations that are aligned with the rear end sections of the long holes; a pair of support capsules that are fastened to the non-dropping bracket in the rear end sections of the long holes in the non-dropping bracket, and that comprise through holes that penetrate in the vertical direction, the support capsules being capable of displacing in the forward direction along the long holes due to an impact load in the forward direction that is applied to these support capsules, and the support capsules are being arranged such that the capsules do not come out from the long holes in the thickness direction of the top plate of the non-dropping bracket; and a pair of connection members (47, 57) that connect the dropping bracket to the support capsules by being inserted into the installation holes in the dropping bracket and into the through holes in the support capsules. a non-dropping bracket that is fastened to and supported by a vehicle body and located on the upper part of a middle section in the axial direction of a steering column, and that comprises a top plate that is provided in the axial direction of the steering column, and a pair of long holes formed in part of the top plate such that the long holes are parallel to each other, and extend in the axial direction of the steering column; a dropping bracket that is supported by the middle section in the axial direction of the steering column, and that comprises a bottom plate whose top surface faces the bottom surface of the top plate of the non-dropping bracket, and a pair of installation holes that are formed in part of the bottom plate in locations that are aligned with the rear end sections of the long holes; a pair of support capsules that are fastened to the non-dropping bracket in the rear end sections of the long holes in the non-dropping bracket, and that comprise through holes that penetrate in the vertical direction, the support capsules being capable of displacing in the forward direction along the long holes due to an impact load in the forward direction that is applied to these support capsules, and the support capsules are being arranged such that the capsules do not come out from the long holes in the thickness direction of the top plate of the non-dropping bracket; and a pair of connection members (47, 57) that connect the dropping bracket to the support capsules by being inserted into the installation holes in the dropping bracket and into the through holes in the support capsules.