  In this paper, we study the problem of energy conservation for the solutions
to the incompressible viscoelastic flows. First, we consider Leray-Hopf weak
solutions in the bounded Lipschitz domain $\Omega$ in $\mathbb{R}^d\,\, (d\geq
2)$. We prove that under the Shinbrot type conditions $ u \in
L^{q}_{loc}\left(0, T ; L^{p}(\Omega)\right) \text { for any }
\frac{1}{q}+\frac{1}{p} \leq \frac{1}{2}, \text { with } p \geq 4,\text{ and }
{\bf F} \in L^{r}_{loc}\left(0, T ; L^{s}(\Omega)\right) \text { for any }
\frac{1}{r}+\frac{1}{s} \leq \frac{1}{2}, \text { with } s \geq 4 $, the
boundary conditions $u|_{\partial\Omega}=0,\,\,{\bf F}\cdot
n|_{\partial\Omega}=0$ can inhibit the boundary effect and guarantee the
validity of energy equality. Next, we apply this idea to deal with the case
$\Omega= \mathbb{R}^d\,\,(d=2, 3, 4)$, and showed that the energy is conserved
for $u\in L_{loc}^{q}\left(0,T;L_{loc}^{p}\left(\mathbb{R}^{d}\right)\right)$
with $ \frac{2}{q}+\frac{2}{p}\leq1, p\geq 4 $ and $
  {\bf F}\in
L_{loc}^{r}\left(0,T;L_{loc}^{s}\left(\mathbb{R}^{d}\right)\right)\cap
L^{\frac{4d+8}{d+4}}\left(0,T;L^{\frac{4d+8}{d+4}}\left(\mathbb{R}^{d}\right)\right)$
with $\frac{2}{r}+\frac{2}{s}\leq1, s\geq 4 $. This result shows that the
behavior of solutions in the finite regions and the behavior at infinite play
different roles in the energy conservation. Finally, we consider the problem of
energy conservation for distributional solutions and show energy equality for
the distributional solutions belonging to the so-called Lions class $L^4L^4$.
