Summary: An associative algebra \(R\) is called an Armendariz algebra if, for any polynomials \(f(x)=a_0+a_1 x +\dots + a_m x_m\) and \(g(x) = b_0 + b_1 x + \dots + b_n x_n \in R[x]\), the equation \(f(x)g(x) = 0\) implies \(a_i b_j = 0\) for all \(i = 0, 1, \dots, m\), \(j = 0, 1, \dots, n\). We describe varieties of associative algebras over a field such that all subdirectly irreducible algebras of the variety are Armendariz.