Abstract A detailed comparison of the accuracy of several popular micromechanical schemes utilized for prediction of the effective elastic properties of materials with parallel cracks is presented. In particular, the non-interaction, Mori–Tanaka, differential and self-consistent schemes are compared against the direct finite element simulations. The latter are performed on the periodic representative volume elements containing 30 strongly oblate spheroids representing the penny-shaped cracks. This work extends the existent results to a more general class of matrix materials – orthotropic materials, which requires the ability to calculate the Eshelby tensor for an ellipsoid in non-isotropic matrix. In addition to the implementation of the integration procedure used for the Eshelby tensor calculation, this work also presents a variation of the Random Sequential Adsorption algorithm modified for periodic structures. Analysis of the results indicates that in the case of parallel nearly flat cracks (strongly oblate spheroids) the overall out-of-plane moduli are best predicted by the differential scheme. On the other hand, Mori–Tanaka scheme should be used for estimation of the in-plane moduli. It also appears that as the cracks are inflated from strongly oblate spheroids to slightly deformed spheres, the best choice of the micromechanical scheme for the out-of-plane properties gradually shifts towards Mori–Tanaka.