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In this paper, we prove new embedding theorems for generalized anisotropic Sobolev spaces, $W_{{\Lambda }^{p,q}\left(w\right)}^{r_1,\cdots ,r_n}$ and $W_X^{r_1,\cdots ,r_n}$, where ${\Lambda }^{p,q}\left(w\right)$ is the weighted Lorentz space and $X$ is a rearrangement invariant space in ${ℝ}^n$. The main methods used in the paper are based on some estimates of nonincreasing rearrangements and the applications of $B_p$ weights.