We investigate when the .product of two smooth manifolds admits a weakly Lagrangian embedding. Assume M, N are oriented smooth manifolds of dimension m and n,. respectively, which admit weakly Lagrangian immersions into

and

. If m and n are odd, then

admits a weakly Lagrangian embedding into

In the case when m is odd and n is even, we assume further that

(N) is an even integer. Then

admits a weakly Lagrangian embedding into

. As a corollary, we obtain the result that

,

>1, admits a weakly Lagrang.ian embedding into

if and only if some ni is odd.