The main results are concerned with sequences of negatively associated random variables. The author proves some upper estimates for \(P\{| S_n|\geq\lambda\}\), \(E| S_n|\), and \(E(\max_{1\leq n\leq k}| S_n|)\), where \(S_n= X_1+\cdots+ X_n\) is the sum of negatively associated random variables. Based on these inequalities a version of the weak invariance principle for strictly stationary negatively associated sequences of random variables is proved. Before proving the invariance principle, the author constructs a sequence of random variables of such a type. Point out the inequality \[ E| S_n|^p\leq C_pn^{p/2-1} \sum^n_{k=1} E| X_k|^p \] (\(C_p\) is a constant depending only upon \(p\geq 2\)), as a typical result.