We present a systematical study of two-body and three-body charmless baryonic B decays. The branching ratios for two-body modes are in general very small, typically less than ${10}^{\ensuremath{-}6},$ except that $\mathcal{B}{(B}^{\ensuremath{-}}\ensuremath{\rightarrow}p{\overline{\ensuremath{\Delta}}}^{\ensuremath{-}\ensuremath{-}})\ensuremath{\sim}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ In general, $\overline{B}\ensuremath{\rightarrow}N\overline{\ensuremath{\Delta}}>\overline{B}\ensuremath{\rightarrow}N\overline{N}$ due to the large coupling constant for ${\ensuremath{\Sigma}}_{b}\ensuremath{\rightarrow}B\ensuremath{\Delta}.$ For three-body modes we focus on octet baryon final states. The leading three-dominated modes are ${B}^{0}\ensuremath{\rightarrow}p\mathrm{n\ifmmode \bar{}\else \={}\fi{}}{\ensuremath{\pi}}^{\ensuremath{-}}({\ensuremath{\rho}}^{\ensuremath{-}}),$ $n\overline{p}{\ensuremath{\pi}}^{+}({\ensuremath{\rho}}^{+})$ with a branching ratio of order $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for ${B}^{0}\ensuremath{\rightarrow}p\mathrm{n\ifmmode \bar{}\else \={}\fi{}}{\ensuremath{\pi}}^{\ensuremath{-}}$ and $8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for ${B}^{0}\ensuremath{\rightarrow}p\mathrm{n\ifmmode \bar{}\else \={}\fi{}}{\ensuremath{\rho}}^{\ensuremath{-}}.$ The penguin-dominated decays with strangeness in the meson, e.g., ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}p\overline{p}{K}^{\ensuremath{-}(*)}$ and ${B}^{0}\ensuremath{\rightarrow}p\mathrm{n\ifmmode \bar{}\else \={}\fi{}}{K}^{\ensuremath{-}(*)},$ $n\mathrm{n\ifmmode \bar{}\else \={}\fi{}}{K}^{0(*)},$ have appreciable rates and the $N\overline{N}$ mass spectrum peaks at low mass. The penguin-dominated modes containing a strange baryon, e.g., ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{0}\overline{p}{\ensuremath{\pi}}^{+},$ ${\ensuremath{\Sigma}}^{\ensuremath{-}}\mathrm{n\ifmmode \bar{}\else \={}\fi{}}{\ensuremath{\pi}}^{+},$ have branching ratios of the order of $(1--4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ In contrast, the decay rate of ${B}^{0}\ensuremath{\rightarrow}\ensuremath{\Lambda}\overline{p}{\ensuremath{\pi}}^{+}$ is smaller. We explain why some of the charmless three-body final states in which baryon-antibaryon pair production is accompanied by a meson have a larger rate than their two-body counterparts: either the pole diagrams for the former have an antitriplet bottom baryon intermediate state, which has a large coupling to the B meson and the nucleon, or they are dominated by the factorizable external W-emission process.