A powdery material particularly useful as a modifier for cementitious materials. This material is a particulate acrylic polymer of a core-shell structure in which the core is made of an acrylic polymer having a glass transition temperature (Tg) of -20 to +15 DEG C, a weight-average molecular weight of 100,000 to 2,000,000 and an acid value of 25 mgKOH/g or below while the shell is made of an acrylic polymer having a Tg of 50 to 90 DEG C, a weight-average molecular weight of 100,000 to 2,000,000 and an acid value of 30 to 130 mgKOH/g, and which has a mean particle diameter of 200 to 700 nm and a core/shell weight ratio of 30/70 to 80/20 (% by weight).