We developed a biophysically-detailed model of the macaque auditory thalamocortical circuits, including primary auditory cortex (A1), medial geniculate body (MGB) and thalamic reticular nuclei (TRN), using the NEURON simulator and NetPyNE multiscale modeling tool. We simulated A1 as a cortical column with a depth of 2000 μm and 200 μm diameter, containing over 12k neurons and 30M synapses. Neuron densities, laminar locations, classes, morphology and biophysics, and connectivity at the long-range, local and dendritic scale were derived from published experimental data. The A1 model included 6 cortical layers and multiple populations of neurons consisting of 4 excitatory and 4 inhibitory types, and was reciprocally connected to the thalamus (MGB and TRN) mimicking anatomical connectivity. MGB included core and matrix thalamocortical neurons with layer-specific projection patterns to A1, and thalamic interneurons projecting locally. Auditory stimulus related inputs were simulated using phenomenological models of the cochlear auditory nerve and the inferior colliculus, which served as input to MGB. The model generated cell type and layer-specific firing rates consistent with overall ranges observed experimentally, and accurately simulated the corresponding local field potentials (LFPs), current source density (CSD), and electroencephalogram (EEG) signals. Laminar CSD patterns during spontaneous activity and responses to speech input were similar to those recorded experimentally. Physiological oscillations emerged spontaneously across frequency bands without external rhythmic inputs and were comparable to those recorded in vivo. We used the model to unravel the contributions from distinct cell type and layer-specific neuronal populations to oscillation events detected in CSD, and explore how these relate to the population firing patterns. Overall, the computational model provides a quantitative theoretical framework to integrate and interpret a wide range of experimental data in auditory circuits. It also constitutes a powerful tool to evaluate hypotheses and make predictions about the cellular and network mechanisms underlying common experimental measurements, including MUA, LFP and EEG signals.