Abstract: The Terzaghi unidirectional consolidation differential equation has long been dominant in the soil consolidation theory and practices.Its classical solution is on the basis of the ideal boundary conditions, which do not accord with those of the common soil layers.Based on the special regularity of the unidirectional permeation and consolidation of saturated soil, this paper avoids the conditions of drainage and impermeation at the bottom boundary, in a simplified assumption for initial and boundary conditions, to find the alternative Laplace solution for the Terzaghi unidirectional consolidation differential equation.A conclusive formula about the excess hydrostatic pressure u, consolidating degree U and average consolidating degree U is obtained.The analysis and discussion on the solution by corresponding curves have concluded that the assumption for initial and boundary conditions is practical and the conclusive formula objectively reflects the regularity of soil consolidating process.