We present measurements and a theoretical analysis of the magnetic properties of dilute neutral (In) donors in CdS, which we demonstrate to be a well‐characterized example of an amorphous antiferromagnet with spins S=1/2. High‐quality data for relative values of sample magnetization have been obtained by the Faraday rotation method at temperatures ranging from 55 mK to 2.5 K and fields up to 15 kG. Data are given for crystals with neutral donor concentrations of 8⋅1016/cm3and 2.1⋅1017/cm3. The susceptibility, &khgr;, increases monotonically with decreasing T with no evidence of ordering, even though the median exchange coupling is ∼7 K. A model Hamiltonian is derived by scaling calculations of direct exchange for the H2molecule to the Bohr radius and effective Rydberg of the donor wave functions. A sample of such a Hamiltonian is generated in a computer simulation and solved approximately by dividing the system into clusters (and isolated spins) according to a coupling threshold and solving the cluster Hamiltonians exactly. Inter‐cluster interactions are included in a molecular field approximation. Excellent agreement with experiment is found, and &khgr; is shown to be dominated by clusters, both even and odd, at all temperatures.