Radiation Shielding Concrete is mixture of cement, water, and heavy weight Aggregates (Fillers) commonly used as Shielding against Radiation as Neutrons that emitted in different facilities as the Medical units, Particle Accelerators. Neutrons causing extra doses to the patient and the Occupational workers which is the main issue to grantee Radiation Safety. Various special Concretes containing Fillers have been produced and used for enhancing the Radiation Shielding Characteristics of the Ordinary Concrete. Only light elements as boron and hydrogen acts as moderate for neutrons that can absorb them. Therefore, for neutrons radiation shielding; concrete must contain light elements beside the heavy elements. Many softwires were employed to examine the effectiveness of the concretes as a radiation shielding materials, also Monte Carlo (MC) simulation program that simulates the transmission and interaction of radiation with different matters. Those Software and simulation programs can be used in different fields such as, Radiation physics, Medicine, and Researches. In this Paper different Fillers added to the Ordinary Concrete and different measuring Methods will be reviewed.