WE ANALYZED THE ASYMPTOTIC SOLUTIONS OF SPHERICAL SHELL OF ARBITRARY THICKNESSES MADE OF AN ELASTIC NEO-HOOKEAN MATERIAL WHICH IS SUBJECTED TO AN EXTERNAL HYDROSTATIC PRESSURE. IN ORDER TO VIEW THE BOUNDARY LAYER BETWEEN THE OUTER REGION (A1-1=O(1)) AND INNER REGION (A1- 1=O (1=N)), FIRST WE GAVE DESCRIPTION OF THE RESULTS OBTAINED BY USING THE WKB METHOD FOREIGN-VALUE EQUATIONS OF THE SPHERICAL SHELL, IT IS CLEAR THAT THE RESULTS OF THIS METHOD ON THE MENTIONED REGIONS ARE NOT EXACTLY MATCH. IN ORDER TO CONSIDER THIS BOUNDARY LAYER (I.E. A THIN LAYER) BETWEEN THE TWO INNER AND OUTER REGIONS WHICH WAS ANALYZED BY WKB METHOD, IT IS NECESSARY TO RECONSIDER THIS LAYER ON THE THIN REGIONS AND FOR MATCH OF TWO INNER AND OUTER SOLUTIONS, WE HAVE TO USE THE THEORY OF BOUNDARY LAYER AND ALSO VAN DYKE'S MATCHING RULE.