Abstract: Concrete with cracks is considered to be a two-phase composite material with a porous matrix and cracks. The interaction direct derivative (IDD) expression was used to estimate the effective permeability of periodic crack model. The conventional seepage numerical analysis method associated with continuous solid elements has some difficulties in mesh coordination, so a new method which combines embedded element technique with elastic analogy was developed to solve this problem. Based on the assumption of penny cracks, a model with three dimensional periodic microstructures was carried out to represent the geometric arrangement of cracks, and the effect of different geometric factors, namely crack diameter, crack density, structure periodicity, crack inclination, and space interval, were studied. The numerical result derived from the new method, was compared with the theoretical solution from IDD. The results reveal that the IDD-derived solution is suitable for low crack density, but it starts to underestimate the finite element results at higher crack density, especially when cracks are nearly touching. During their approach to each other, the effective permeability can be described by an asymptotic logarithmic expression.