We present a numerical study of the effect of a free-energy anisotropy of the solid-solid interphase boundaries on the formation of tilted lamellar microstructures during directional solidification of nonfaceted binary eutectic alloys. We used two different methods – phase-field (PF) and dynamic boundary-integral (BI) – to simulate the growth of periodic eutectic patterns in two dimensions. For a given Wulff plot of the interphase boundary, which characterizes a eutectic grain with a given relative orientation of the two solid phases, the lamellar tilt angle depends on the angle between the thermal axis z and a reference crystallographic axis. Both PF and BI results confirm the general validity of a recent approximate theory which assumes that, at the trijunctions, the surface tension vector of the interphase boundary is parallel to z. In particular, a crystallographic locking of the lamellae onto a direction close to a deep minimum in the Wulff plot is well reproduced in the simulations.