A cellular array multiplier for performing the multiplication of two elements in the finite field GF($2^m$) is presented in this paper. This multiplier is consisted of three operation part ; the multiplicative operation part, the modular operation part, and the primitive irreducible polynomial operation part. The multiplicative operation part and the modular operation part are composed by the basic cellular arrays designed AND gate and XOR gate. The primitive iirreducible operation part is constructed by XOR gates, D flip-flop circuits and a inverter. The multiplier presented here, is simple and regular for the wire routing and possesses the properties of concurrency and modularity. Also, it is expansible for the multiplication of two elements in the finite field increasing the degree m and suitable for VLSI implementation.