  The cosmological singularities of the Bianchi I universe are analyzed in the
setting of loop geometry underlying the loop quantum cosmology. We solve the
Hamiltonian constraint of the theory and find the Lie algebra of elementary
observables. Physical compound observables are defined in terms of elementary
ones. Modification of classical theory by holonomy around a loop removes the
singularities. However, our model has a free parameter that cannot be
determined within our method. Testing the model by the data of observational
cosmology may be possible after quantization of our modified classical theory.
