We consider the Lauricella hypergeometric function (Formula presented.), depending on (Formula presented.) variables (Formula presented.), and obtain formulas for its analytic continuation into the vicinity of a singular set which is an intersection of the hyperplanes (Formula presented.). It is assumed that all N variables are large in modulo. This formulas represent the function (Formula presented.) outside of the unit polydisk in the form of linear combinations of other N-multiple hypergeometric series that are solutions of the same system of partial differential equations as (Formula presented.). The derived hypergeometric series are N-dimensional analogues of the Kummer solutions that are well known in the theory of the classical hypergeometric Gauss equation. © 2021 Informa UK Limited, trading as Taylor & Francis Group.