The effects of uniaxial strain and hydrostatic pressure on Hg 0.83 Re 0.18 Ba 2 Ca 2.4 Cu 3.6 O 14 [Hg 0.83 (Re 0.18)-1223] were investigated by AC magnetic measurements under stress corresponding to a pressure of 20 GPa at maximum. According to a previous thermal study based on the Ehrenfest relation, in-plane contraction should increase the superconducting transition temperature (T c), whereas out-of-plane contraction should decrease T c. This suggests that the increase in T c under hydrostatic-pressure contraction must be smaller than that under in-plane contraction. However, the present uniaxial-strain experiments revealed enhancement of T c under both in-plane and out-of-plane contraction, and the largest enhancement was observed under hydrostatic-pressure contraction. According to a band calculation, all contraction styles induce hole doping from the HgO blocks to the CuO 2 blocks, and hydrostatic-pressure contraction yields the largest hole doping among three contractions. This behavior explains well a series of changes in T c in the stress region of below 8 GPa. More specifically, under hydrostatic-pressure contraction, T c exhibited an increase, a decrease, and another increase with increasing pressure, and this multistep change is similar to that observed in Bi-2223-type cuprate superconductors, suggesting that it is necessary to distinguish the effect of strain on the middle CuO 2 plane in the three-CuO 2-plane package from that on the outer planes.