  In recent years there has been a growing interest in the field of wormhole
physics in the presence of the Casimir effect. As this effect provides negative
energy density, it can be utilized as an ideal candidate for the exotic matter
required for creating a traversable wormhole. In the context of modified
theories of gravity such as Brans-Dicke (BD) theory \cite{BDTH}, wormhole
geometries {have} been vastly investigated{. However}, the scientific
literature is silent on the issue of BD wormholes in the presence of Casimir
energy. Our aim in the present study is to seek for static spherically
symmetric solutions representing wormhole configurations in BD theory with
Casimir energy as the supporting matter. The Casimir {setup} we assume
comprises two electrically neutral, infinitely large parallel planes placed in
a vacuum. We then consider the Casimir vacuum energy density of a scalar field
in such a configuration with Dirichlet {and} mixed boundary conditions. In the
former case, the corresponding Casimir force is attractive and in the latter
this force is repulsive. We present exact zero tidal force wormhole solutions
as well as those with non-vanishing redshift function for both types of Casimir
energies. The conditions on wormhole solutions along with the weak (WEC) and
null (NEC) energy conditions put constraints on the values of BD coupling
parameter. These constraints are also subject to the value of BD scalar field
at the throat and the throat radius. We therefore find that BD wormholes in the
presence of Casimir energy can exist without violating NEC and WEC (for the
repulsive Casimir force). Finally, we examine the equilibrium condition for the
stability of the obtained solutions using Tolman-Oppenheimer-Volkoff (TOV)
equation.
