Tilted coil models are incorporated in a Volume Integral Method code for realistic simulations of eddy current inspections. The coils have either cylindrical or rectangular shapes and the configurations involve a layered conductor system with an arbitrary number of layers. Emphasis is put on the rapid calculation of the incident fields by modifying existing integral expressions to equivalent Fourier-type series expressions. In this paper we present only the cylindrical coil configuration. Theoretical results for the crack signal of a titled coil are verified by experimental measurements.