  We introduce and analytically solve a directed sandpile model with stochastic
toppling rules. The model clearly belongs to a different universality class
from its counterpart with deterministic toppling rules, previously solved by
Dhar and Ramaswamy. The critical exponents are D_||=7/4, \tau=10/7 in two
dimensions and D_||=3/2, \tau=4/3 in one dimension. The upper critical
dimension of the model is three, at which the exponents apart from logarithmic
corrections reach their mean-field values D_||=2, \tau=3/2.
