Constrained sintering of substrates with a laminate structure that have an inner-self-constraining alumina layer laminated between two glass-alumina mixed layers has been studied. The influence of the particle size of alumina in the glass-alumina mixed layer's upon firing shrinkage was investigated. Sintering shrinkage in the x-y direction of the substrate decreased with increasing the particle size of alumina in glass-alumina mixed layers. Penetration length of glass to the inner-self-constraining alumina layer increased with increasing particle size of alumina in glass-alumina mixed layers. It was considered that sintering shrinkage in the x-y direction of the substrate and penetration length of a glass into alumina layer will be dependent on the coverage of alumina particles on surface of glass particles. As for the particle size of alumina in glass-alumina mixed layers, it is desirable for it to be the same as the particle size of glass and the coverage of the surface of glass particle with alumina particles should be less than 17.5% in the case of constrained sintering of substrates with an inner-self-constraining alumina layer. Sintering shrinkage in the x-y direction was less than 0.2%.