We have proposed a thermoacoustic Stirling refrigerator which has a potentially long life and can be produced low cost. The refrigerator consists of a looped tube of about one wave length including a regenerator that connects via a branch tube to an oscillating device at the opposite end. To investigate the proper geometry for an efficient refrigerator, we have analyzed the acoustic wave in the simplified refrigerator model under uniform temperature conditions, obtaining useful data on the effects of regenerator position and branch tube length. The maximal value of the acoustic intensity in the regenerator is taken when the regenerator is located 40 to 45% of the looped tube from the branch. The minimal value of the acoustic intensity in the regenerator is taken when the regenerator is located at around 5% of the looped tube from the branch. Through our experiments, we have confirmed that the refrigeration effect is deeply dependent on the acoustic intensity in the regenerator and the data on the proper regenerator position. The experimental data on the effect of branch length agree with the analytical data qualitatively, but not quantitatively. It is suggested from the analytical data on the velocity in the regenerator that the cause of the discrepancy be due to the regenerator loss caused by incomplete heat exchange between regenerator and fluid.