We generalize the mass transference principle established by Beresnevich &Velani to limsup sets generated by rectangles.More precisely,let fxngn≥1 be a sequence of points in the unit cube [0,1]d with d ≥ 1 and frngn≥1 a sequenceof positive numbers tending to zero.Under the assumption of full Lebesguemeasure theoretical statement of the set{x ∈2 [0,1]d:x ∈ B(xn,rn),for infinitely many n ∈ N}.we determine the lower bound of the Hausdorff dimension and Hassdorff measure of the set {x ∈ [0,1]d:x ∈ Ba(xn,rn),for infinitely many n ∈ N}.where a = (a1,...,ad) with 1 ≤ a1 ≤ a2 ≤...≤ ad and Ba(x,r) denotes a rectanglewith center x and side-length (ra1,ra2,...,rad).When a1 = a2 =...= ad,the result is included in the setting considered by Beresnevich & Velani.