At first blush, the goal in designing and building toolholders is simple: Design a device that can hold a tool with enough rigidity for its particular application and so that it can maintain accuracy in a wide variety of machining conditions. More needs to be done. make it easy to use so change-outs are quick and accurate. And help it extend tool life and improve finish quality if you can. Described principle of work of the instrumental clamping chuck (ІCC) with gidroplast, created with the use of genetic-morphological the approach and the executed theoretical analysis of internal stress, and moving of basic clamping element - cylindrical thin-walled plug. For the theoretical analysis compiled the normal scheme of loading of the cylindrical thin-walled plug in longitudinal and cross sections elastic a place with three zones of variable length and thickness, and one thickness on all length of a place for the purpose of search of rational design construction parameters. For the solution of a task have been used the formulas to Lama and rejected infinitesimal quantities of high orders in comparison with other. Recommendations about the choice of design data of the cylindrical thin-walled plug are offered and theoretically proved – 1) tension at all points walled sleeve - negative, corresponding to compression; 2) accepted - thick-walled cylindrical sleeve T1 = 0.52 mm; 3) use of material for plug - Steel 40X GOST 8731-87 with heat treatment, hardening and heating microwave h 1,8 ... 2,2; supply - HRC 35 ... 40