An alloy of composition Al-12.6 wt.% Si was prepared using metals of 99.99% purity. Weighed amounts of aluminium and silicon were melted in the vacuum-melting furnace. This irregular eutectic alloys were directionally solidified upward with a constant growth rate V (8.3 x 10(-3) mm/s) and different temperature gradients G (2.0-7.8 K/mm) and also with a constant temperature gradient G (7.8 K/mm) and different growth rates V (8.3-498.7 x 10(-3) mm/s) in the directional solidification furnace. The interflake spacings lambda and microhardness H-nu were measured from both transverse section and longitudinal section of the specimen. The variations of H, with respect to G, V, and lambda have been determined by using the linear regression analysis method. It has been shown that H-nu increases with the increasing values of G and V. On the other hand H-nu values decreases with the increasing lambda values. The Hall-Petch type relationships obtained in this work have been compared with the previous works.