A linear elastic fracture mechanics (LEFM) model for the engineering fracture design of cement sheath integrity at early ages in oil and gas well applications is proposed. The model considers the specific worst-case scenario of a single radial crack and estimates the energy release rate (stress intensity factor) that potentially develops in a cement sheath as a result of the buildup of eigenstresses at early ages, considering the loss of axisymmetry. Specifically, the model involves a two-step solution procedure: a chemoelastic stress solver and a LEFM solver using an Airy-stress function approach together with the method of complex variables. For the first, an appropriate constitutive model for cement slurries at early ages is required as a backbone for chemoelastic stress development. Second, the LEFM solver uses the stresses to estimate the energy release rate and the stress intensity, and thus provide a means to evaluate the driving force of fracture propagation and the fracture risk as a function of the degree of hydration. The functional relationships thus established between the LEFM quantities and the degree of the chemical reaction are expected to become an indispensable tool in safely designing well cements for operation under extreme bore hole conditions.