The purpose of this report is to describe the shielding calculations and techniques used in sizing the MMSR primary shield, the results obtained, and the resulting shield thicknesses. The present report covers many of the items scheduled for presentation in the final MMSR shield design report to be issued in November of 1958. The primary shield in the MMSR consists of the reflector, thermal shields, pressure vessel wall, a 33" water annulus and a layer of lead shielding at the exterior of the primary shield tank vary from 3" to 1" in thickness.