  The problem of predicting the growth of a system of cracks, each crack
influencing the growth of the others, arises in multiple fields. We develop an
analytical framework toward this aim, which we apply to the `En-Passant' family
of crack growth problems, in which a pair of initially parallel, offset cracks
propagate nontrivially toward each other under far-field opening stress. We
utilize boundary integral and perturbation methods of linear elasticity, Linear
Elastic Fracture Mechanics, and common crack opening criteria to calculate the
first analytical model for curved En-Passant crack paths. The integral system
is reduced under a hierarchy of approximations, producing three methods of
increasing simplicity for computing crack paths. The last such method is a
major highlight of this work, using an asymptotic matching argument to predict
crack paths based on superposition of simple, single-crack fields. Within the
corresponding limits of the three methods, all three are shown to agree with
each other. We provide comparisons to exact results and existing experimental
data to verify certain approximation steps.
