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In the proposed element-free Galerkin method for deforming multiphase porous media, displacement of the porous-solid skeleton is modelled by standard finite elements while wetting and non-wetting fluid pore pressures are included as element-free nodes. The matrix formulation is derived from the variational formulation of the multiphase governing equations. The case of a domain with a material or field discontinuity is handled by using Lagrange multipliers. One- and two-dimensional applications are presented for which the results, compared with those obtained by either the closed-form solution standard finite-element approach or experimental tests, show the efficiency of the proposed technique. The necessity of taking air pore pressure into account for partially saturated soils is discussed: free surface capturing is analysed and the problem of its intersection with outer boundaries (so-called seepage surface) is studied. © 1998 John Wiley & Sons, Ltd.