Abstract: A process for the preparation of soft porous sheets, comprises forming into a sheet a composition comprising (i) 40 to 80% by weight of an inorganic filler and (ii) 60 to 20% by weight of a polyolefin type thermoplastic elastomer composition comprising at least 50% by weight of a polyolefin type thermoplastic elastomer substantially free of a polar group, in which the tensile stress at a temperature of 25.degree. C. under 100% stretching (100% modulus) is 10 to 100 Kg/cm.sup.2, the elongation at break under stretching is at least 100% and the permanent strain under 100% stretching is less than 50% and up to 50% by weight of a thermoplastic plastomer, and stretching the sheet at a temperature lower than the softening temperature of the polyolefin type thermoplastic elastomer. A porous sheet obtained according to this process has a good combination of flexibility, air permeability and water resistance.