The thalamus plays a crucial role in modulating the cortical activity underlying sensory and cognitive processes. In particular, recent experimental findings highlighted that the thalamus does not merely act as a binary gate for sensory stimuli, but rather participates to the processing of sensory information. Clarifying such thalamic influence on cortical dynamics is also important as the thalamus is the target of therapies such as DBS for Tourette patients. In this perspective, various computational models have been proposed in the last decades. However, a detailed description of the propagation of thalamic activity to the cortex is missing. Here we present a simple computational model of thalamocortical connectivity accounting for the propagation of activity from the thalamus to the cortex. The model includes both the single-neuron scale and the mesoscopic level of Local Field Potential (LFP) signals. Numerical simulations at both levels reproduce typical thalamocortical dynamics which are consistent with experimental measurements and robust to parameters changes. In particular, our model correctly reproduces locally generated rhythms as spindle oscillations in the thalamus and gamma oscillations in the cortex. Our model paves the way to deeper investigations of the thalamic influence on cortical dynamics, with and without sensory inputs or therapeutic electrical stimulation.