Directional solidification of lamellar eutectic has been studied both theoretically and experimentally. This process has been modeled through comparing it with directional solidification of an array of cells in binary alloys and developing of the Saffman-Taylor viscous fin-gerinig in a Hele-Shaw cell in an unitied framework. A coupling relation among the solute diffusion, the thermal transfer and the capillary effect of the growing interface has been derived. The well known scaling law λ2V = const can be derived from this relation. Directional solidification of regular Al-Al2Cu eutectic and irregular Al-Si eutectic has been investigated experimentally, the coupling relation has been verified. The solidifying interface profile and thermal transfer effect of solidification have also been discussed.