A tube support plate is disclosed for supporting a plurality of tubes with reduced vibration in a nuclear steam generator. The support plate has a plurality of holes disposed therethrough in a regular array. Each hole has an axis, an interior surface and a plurality of lands supported on the interior surface and extending towards the axis. The support plate has a given thickness as taken along the hole axis, and each of the lands has a tapered surface for facilitating tube insertion. The method of forming the tube support plate comprises a first step of forming each of the holes through the support plate with a first cylindrical portion of a first diameter and a second cylindrical portion of a second diameter less than the first diameter. Next, portions of the second cylindrical portion are removed in a second step to form a plurality of lands having exposed ends supporting a tube within the hole.