We report the results of a search for the rare baryonic decay modes B -> Lambda Lambdabar, B -> Lambdabar p, B -> Lambdabar p pi, and B -> p pbar using 5.8M BBbar pairs collected with the CLEO detector. We see no statistically significant signals in any of these modes and set 90% confidence level upper limits on their branching fractions, B(B -> Lambda Lambdabar) < 3.9 times 10^{-6}, B(B -> Lambdabar p) < 2.6 times 10^{-6}, B(B -> Lambdabar p pi) < 1.3 times 10^{-5}, and B(B -> p pbar) < 7.0 times 10^{-6}.
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