  For the B-type supergiant $\kappa$ Cassiopeiae (HD 2905) variabilities with
periods between several hours and a few days have been observed both
photometrically and spectroscopically. A recent study of this star by
Sim\'on-D\'{\i}az et al. (2018) has revealed variability with a dominant period
of 2.7 days. To understand this variability, we present a linear non-adiabatic
stability analysis with respect to radial perturbations for models of $\kappa$
Cassiopeiae. Instabilities associated with the fundamental mode and the first
overtone are identified for models with masses between 27 M$_{\odot}$ and 44
M$_{\odot}$. For selected models, the instabilities are followed into the
non-linear regime by numerical simulations. As a result, finite amplitude
pulsations with periods between 3 and 1.8 days are found. The model with a mass
of 34.5 M$_{\odot}$ exhibits a pulsation period of 2.7 days consistent with the
observations. In the non-linear regime, the instabilities may cause a
substantial inflation of the envelope.
