For the blocking flowshop group scheduling problem (BFGSP), this study addresses its high computational burden associated with insertion operations due to over-much objective function calculations as the number of groups and jobs increases. Unfortunately, the existing rapid evaluation methods exhibit limitations when handling group-based insertion, blocking constraint, total flow time, and total tardiness time criteria. We emphasize the need for improved rapid evaluation techniques tailored to these limitations and propose the theoretical analysis and methods of a critical machine-based rapid evaluation for total flow time and tardiness criteria of BFGSP. More specifically, first, under the two scenarios of the group and job scheduling, we propose the concept of the critical machines, three theorems, one corollary, and their corresponding proofs, respectively. Secondly, we present rapid evaluation methods for group insertion and job insertion, respectively, namely Rapid_group and Rapid_job based on the above theorems and corollary. We find that it is unnecessary to start the computation from the first machine when scheduling the changed groups or jobs, and it suffices to begin the computation from the critical machine, thus reducing the computational cost. Finally, we conduct five experiments on four well-known benchmarks (a total of 6000 instances). Through statistical analysis, it becomes evident that our computational efforts have decreased significantly in computing both the total flow time and the total tardiness time for group-based and jobs-based insertion operations. The development of rapid evaluation mechanisms is a promising approach to mitigate the time complexity by reducing the number of machines involved in the evaluation, and makes up for gaps in existing accelerated evaluation methods for BFGSP.