  In this paper, we obtain some boundedness of the following general
multilinear square functions $T$ with non-smooth kernels, which extend some
known results significantly. $$ T(\vec{f})(x)=\big( \int_{0}^\infty
\big|\int_{(\mathbb{R}^n)^m}K_v(x,y_1,\dots,y_m)
\prod_{j=1}^mf_{j}(y_j)dy_1,\dots,dy_m\big|^2\frac{dv}{v}\big)^{\frac 12}. $$
The corresponding multilinear maximal square function $T^*$ was also introduced
and weighted strong and weak type estimates for $T^*$ were given.
