Coupled Boolean Networks (CBN) are a class of discrete-time dynamical systems with a wide range of applications, ranging from distributed change detection in sensor networks to the identification of cellular patterns in tissue structures, for example. An Attractor Field corresponds to a subset of the state space of a CBN that presents certain stability properties. Attractor Fields can be used to model many events in biological systems, in particular those involving stabilization processes between interacting dynamic biological entities. Hence, an important problem consists of computing the Attractor Fields of a given CBN. Due to the exponential nature of the state space of a CBN, computing Attractor Fields is a computationally intensive task, which is currently feasible only for CBNs of unrealistic small size. In this work, we aim to develop a high-performance method for computing Attractor Fields in CBNs. In order to achieve this, we implemented algorithms based on the multi-core architecture that exploit the parallelizable nature of the problem. The experimental results suggest significant performance gains (speedup between 13 and 14) compared to the existing serial method, especially in Step 1. In addition, we achieved almost linear scalability for this Step 1, which allowed us to propose a fork-join model to optimize the method.