Poroelasticity is an example of coupled processes which are crucial for many applications including safety assessment of radioactive waste repositories. Numerical solution of poroelasticity problems leads to systems of algebraic equations, which may be solved simultaneously or iteratively. In this work, parallel scalability of the monolithic strategy and of the fixed-strain splitting strategy is examined, which depends mostly on linear solver performance. It was expected that splitting strategy would show better scalability due to better performance of a black-box linear solver on systems with simpler structure. However, this is not always the case.