This invention relates to a stack comprising a continuous solid-phase matrix and tubular fuel cells embedded in the matrix. Each fuel cell comprises an inner electrode layer, an outer electrode layer, and an electrolyte layer sandwiched between the inner and outer electrode layers. The matrix is sufficiently porous to allow a first reactant to flow through the matrix and to the outer electrode of each fuel cell, and have sufficient mechanical strength to support the fuel cells in the stack. The fuel cells are embedded such that a second reactant may be flowed through the inside of each tubular fuel cell and to the inner electrode thereof. Alternatively, a stack of tubular separation membranes or a stack of tubular membrane reactors may be embedded in the matrix. The matrix material may comprise solid state foam, metal filament, or metal, cermet, or ceramic wool.