A method of manufacturing a ceramic member composed of a thin plate having a plurality of fine through holes and a rigid plate integrally formed with the thin plate by firing. The thin plate is supported by the rigid plate at least at both sides of a portion where the plurality of fine through holes are formed. A minimum value of the size of the holes is 150 .mu.m or less, a thickness of the thin plate 7 is 100 .mu.m or less, and a minimum value of the interval between adjacent holes is 150 .mu.m or less. A tensile strength .sigma. of a green sheet for the thin plate is 10 kgf/cm.sup.2 or more and 200 kgf/cm.sup.2 or less. An elongation factor represented by the expression .DELTA.I.multidot.S/T, where .DELTA.I represents an amount (mm) of elongation at rupture; T, a tension (kgf) at rupture; and S, a cross section (mm.sup.2) of the green sheet for the thin plate, is 0.5 mm.sup.3 /kgf or more and 25.0 mm.sup.3 /kgf or less. An absolute value of the difference of pre-sintering temperature T.sub.50 between the green sheet for the thin plate and the green sheet for the rigid plate is 50.degree. C. or less, and an absolute value of the difference of firing shrinkage factor F therebetween is 1.5% or less. The green sheet for the thin plate having the plurality of fine through holes 1 formed by punching thereupon is laminated upon the rigid plate to form an integral laminate, and then fired.