  Minnaert resonance is a well known physical phenomenon and it has many
important applications, in particular in the effective realisation of acoustic
metamaterials using bubbly mediums in recent years. In this paper, motived by
the Minnaert resonance, we consider the low-frequency resonance for acoustic
bubbles embedded in soft elastic materials. This is a hybrid physical process
that couples the acoustic and elastic wave propagations. By delicately and
subtly balancing the acoustic and elastic parameters as well as the geometry of
the bubble, we show that Minnaert resonance can (approximately) occur for
rather general constructions. Our study poses a great potential for the
effective realisation of negative elastic materials by using bubbly elastic
mediums.
