  We theoretically study the formation of single-particle bound states confined
by strain at the center of bubbles in monolayers of transition-metal
dichalcogenides (TMDs). Bubbles ubiquitously form in two-dimensional crystals
on top of a substrate by the competition between van der Waals forces and the
hydrostatic pressure exerted by trapped fluid. This leads to strong strain at
the center of the bubble that reduces the bangap locally, creating potential
wells for the electrons that confine states inside. We simulate the spectrum
versus the bubble radius for the four semiconducting group VI TMDs, MoS$_2$,
WSe$_2$, WS$_2$ and MoSe$_2$, and find an overall Fock-Darwin spectrum of
bubble bound states, characterised by small deviations compatible with Berry
curvature effects. We analyse the density of states, the state degeneracies,
orbital structure and optical transition rules. Our results show that elastic
bubbles in these materials are remarkably efficient at confining photocarriers.
