In this paper, we present numerical modeling aimed to explain Deep Long Period (DLP) events occurring in middle-to-lower crust beneath volcanoes and often observed in association with volcanic eruptions or their precursors. We consider a DLP generating mechanism caused by the rapid growth of gas bubbles in response to the slow decompression of H\textsubscript{2}O–CO\textsubscript{2} over-saturated magma. The nucleation and rapid growth of gas bubbles lead to rapid pressure change in the magma and elastic rebound of the host rocks, radiating seismic waves recorded as DLP events. The magma and host rocks are modeled as Maxwell bodies with different relaxation times and elastic moduli. Simulations of a single sill-shaped intrusion with different parameters demonstrate that realistic amplitudes and frequencies of P and S seismic waves can be obtained when considering intrusions with linear sizes of the order of 100 m. We then consider a case of two closely located sills and model their interaction. We speculate on conditions that can result in consecutive triggering of the bubble growth in multiple closely located batches of magma, leading to the generation of earthquake swarms or seismic tremors.