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Long period seismic events observed under many volcanoes are often interpreted in relation to any fluid-filled resonator. The kinematic mechanisms have been also studied seismologically in terms of seismic moment, and some of them indicate the geometry of a 'tensile' crack. In Volcanology, Chouet (1986) first solved the elasto-dynamic equations coupling with the fluid using a finite difference method, similarly to 'shear' crack problems treated in seismology, and this model is always a reference (Chouet and Motoza, 2013). But only a few studies have treated such dynamic problems (e.g. Yamamoto and Kawakatsu, 2009), while dynamic 'shear' cracks have been studied progressively in these two decades in seismology. This study presents a boundary integral equation method (BIEM) in the time domain to solve a 'tensile' crack resonance. The time-domain BIEM is often used for a 'shear' crack thanks to its accuracy, efficiency and flexibility, and usually adopted with an explicit approach (a time step $\Delta t$ is short enough to an element size $\Delta s$ so that any grid influences instantaneously itself, $\Delta t$ <= $\Delta s$/(2*P-wave velocity) ). However such explicit approach introduces severe high frequency oscillations on a 'tensile' crack whose frictional property is intrinsically different from a 'shear' crack. It is found that the implicit approach can retrieve the expected solution for a longer time step of $2 \Delta t$ and no high-frequency oscillations is visible for a $4 \Delta t$. Comparing to the other methods, the time-domain BIEM is easy to be combined with any boundary condition, so that the method would be widely applicable for the observed long period sources if the geometry of a tensile crack is inferred.