  In the present paper, a class of non-weight modules over the super-BMS$_3$
algebras $\S^{\epsilon}$ ($\epsilon=0$ or $\frac{1}{2}$) are constructed.
Assume that $\mathfrak{t}=\C L_0\oplus\C W_0\oplus\C G_0$ and $\mathfrak{T}=\C
L_0\oplus\C W_0$ are the Cartan subalgebra (modulo center) of $\S^{0}$ and
$\S^{\frac{1}{2}}$, respectively. These modules over $\S^{0}$ when restricted
to the $\mathfrak{t}$ are free of rank $1$, while these modules over
$\S^{\frac{1}{2}}$ when restricted to the $\mathfrak{T}$ are free of rank $2$.
Then we determine the necessary and sufficient conditions for these modules
being simple, as well as determining the necessary and sufficient conditions
for two $\S^{\epsilon}$-modules being isomorphic. %Moreover, we see that the
category of free $U(\mathfrak{t})$-modules of rank $1$ over $\S^0$ is
%equivalent to the category of free $U(\mathfrak{T})$-modules of rank $2$ over
%$\S^{\frac{1}{2}}$.

Representation Theory