The goal of this work is to produce a ceramic waste form that permanently occludes radioactive waste. This is accomplished by absorbing radioactive salts into zeolite, mixing with glass frit, heating to a molten state at 915°C to form a sodalite glass matrix, and solidifying for long-term storage. Less long-term leaching is expected if the solidifying cooling rate does not cause cracking. In addition to thermal stress, this paper proposes a mathematical model for the stress formed during solidification, which is very large for fast cooling rates during solidification and can cause severe cracking. A solidifying glass or ceramic cylinder forms a dome on the cylinder top end. The temperature distribution during solidification causes the solidification stress and the dome resulting in an axial length deficit. The axial stress, determined by the length deficit, remains when the solid is at room temperature with the outer region in compression and the inner region in tension. Large tensions will cause cracking of the specimen. The temperature deficit, derived by dividing the length deficit by the coefficient of thermal expansion, allows solidification stress theory to be extended to the circumferential stress. This paper derives the solidification stress model, gives examples, explains how to induce beneficial stresses, and compares theory to experimental data.