The nucleation and growth of microcracks in elastic lamellar microstructures is studied numerically. The analyses are carried out within a framework where the continuum is characterized by two constitutive relations: one relating the stress and strain in the bulk material and the other relating the traction and separation across a specified set of cohesive surfaces. In such a framework, fracture initiation and crack growth, including micro-crack nucleation ahead of the main crack, arise naturally as a consequence of the imposed loading, without any additional assumptions concerning criteria for crack growth, crack path selection or micro-crack nucleation. Full transient analyses are carried out and plane strain conditions are assumed. The specific problem analyzed is a compact tension specimen with two regions of differing lamellar orientation separated by a fracture resistant layer of finite width d, which is small compared to the physical dimensions of the specimen. An initial crack, normal to the applied loading, is assumed to exist in the first region whose lamellar orientation is fixed. The lamellar orientation of the second region, beta, is varied, as is the thickness of the fracture resistant layer. It is found that microcrack nucleation in the second region is highly sensitive to the lamellar orientation in that region for small values of d. However, microcrack nucleation becomes rather insensitive to beta with increasing d. It is also shown that a linear elastic fracture mechanics model with one adjustable parameter gives good agreement with the numerical results for fracture initiation.