The present invention provides a rigid modular holding with axial and radial compensation for multiple and universal application of all machining processes, engineering, machine building, and construction fields where ever applicable for rotary and static systems. Design of modular holding includes male and female portions (401,301) of joining parts machined to the required shape and clearances to accommodate modular locking rigidly with face butting (407, 308). Radial and axial run out adjustments is controlled by the grub screws (307, 306) and run out compensation can be achieved within micron. An Area used for clamping and designed within the area of joining parts results reduction in material and processing cost. Since, the material is not protruding out from the surface of the joining parts, esthetically looks good and convenient for designing multiple applications as it is not possible at present.