In the field of parallel FEM methods a number of highly efficient solutions for distributed memory systems exist, but the passage to adaptive parallel FEM simulations leads, in all probability, to a more dynamic behaviour with respect to data placement and load balancing. Therefore shared-memory architecture seems to be a more appropriate solution for getting efficient implementations. This paper presents a parallelized CG-method for shared memory systems which was implemented on a 4-processor SMP system and makes explicit use of shared memory to enhance the communication between different domains. It is based on an idea for implementing parallization on distributed memory systems and represents an appropriate modification of this method. The results show that an increased synchronization expense can partially compensate the advantages of shared memory communication depending on the levels of refinement and the processor number.