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The construction of neighbour lists based on the linked cell method is investigated in the context of particle simulation methods within the OpenMP shared memory programming model. Various implementations are studied which avoid memory collisions and race conditions. Performance and optimisation considerations are made along with run time behaviour and memory requirements. Performance models are proposed, which reproduce the measured runtime behaviour and which provide insight into the performance dependence on specific system parameters. Benchmarks are performed for different implementations on a number of multi-core architectures and thread numbers up to 240 are considered on the Xeon Phi architecture in the SMT mode, so that performance can be studied for a large number of threads working concurrently on the construction of linked cells on a shared memory partition.