  We study the three-body charmed baryonic decays $\bar{B}^0\to\Sigma_c^{++}
\bar{p}\pi^-$ and $\bar{B}^0\to\Sigma_c^{0}\bar{p}\pi^+$ in the four-body final
state $\bar{B}^0\to\Lambda_c^{+}\bar{p}\pi^+\pi^-$, using a data sample of 357
fb$^{-1}$ accumulated at the $\Upsilon(4S)$ resonance with the Belle detector
at the KEKB asymmetric-energy $e^+e^-$ collider. We measure the branching
fractions ${\cal B}
(\bar{B}^0\to\Sigma_c(2455)^{++}\bar{p}\pi^-)$=$(2.1\pm0.2\pm0.3\pm0.5)\times
10^{-4}$, ${\cal
B}(\bar{B}^0\to\Sigma_c(2455)^{0}\bar{p}\pi^+)$=$(1.4\pm0.2\pm0.2\pm0.4)\times1
0^{-4}$, ${\cal B}(\bar{B}^0\to\Sigma_c(2520)^{++}
\bar{p}\pi^-)$=$(1.2\pm\0.1\pm0.2\pm0.3)\times10^{-4}$ with statistical
significances of 13.1, 9.5 and 7.2 standard deviations, respectively. The
errors are statistical, systematic, and due to the uncertainty in ${\cal
B}(\Lambda_c^+\to{p}K^-\pi^+)$, respectively. We also set an upper limit ${\cal
B}(\bar{B}^0\to\Sigma_c(2520)^{0}\bar{p}\pi^+)<0.38\times10^{-4}$ at the 90%
confidence level. In addition, we obtain a non-resonant branching fraction of
$(6.4\pm0.4\pm\0.9\pm1.7)\times10^{-4}$, and a total branching fraction of
$(11.2\pm0.5\pm1.4\pm2.9)\times10^{-4}$ for
$\bar{B}^0\to\Lambda_c^{+}\bar{p}\pi^+\pi^-$.
