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YBCO coated conductor (CC) is useful for application to the insert coil for the NMR because of its great property on critical current under high magnetic field. For the safe operation of CC magnets, design of the stabilizer is imperative issue. The minimum quench energy, minimum propagation zone (MPZ), and quench propagation velocity are obviously affected by both properties and thickness of the stabilizer. In this paper, stacks of CCs were used to be partly substituted for a double pancake magnet for simplicity in experiments, and the CCs in a stack were pressed from top and bottom to enhance thermal and electrical contact. The heater made of Hastelloy C-276 was attached to initiate quench. The stacks which comprise only CCs and pairs of CC and additional copper tape were fabricated, and tests of longitudinal and transverse quench propagation in the stack were carried out in both liquid nitrogen (LN2) of 77 K and liquid helium (LHe) of 4.2 K. Copper tapes were attached on each CC without soldering in the stack for the tests to see effects of the thickness of stabilizer and the contact between CC and copper tape. Numerical analysis was performed by using finite element method (FEM). Comparisons of experiment and simulation results were reported and discussed from the point of view of magnet stability and protection.