This work addresses some key guidelines needed for the efficient implementation of algorithms in computational mechanics. The latter primarily encompasses the development of methods for analyzing mechanical systems and the algorithms necessary for their implementation. The implementation of a given method frequently necessitates the application of a broad spectrum of diverse algorithms, which ultimately determine the numerical efficiency of the method. This study focuses on two aspects, which are crucial in processing many objects (large finite element meshes). The first aspect addresses the reduction of the algorithm order since mostly the highest acceptable order is the superlinear one. The second aspect considers processing parallelization where the key issues are minimization of required synchronization between parallel processes and efficient implementation of code blocking mechanisms. The theory discussed is illustrated by a practical numerical example, which demonstrates that both algorithm order reduction and parallelization can dramatically affect the practical applicability of an algorithm in interactive engineering work.