Gas and vapour emissions from subglacial or subnivean volcanoes are capable of melting voids and passageways, here termed glaciovocanic caves and chimneys, in the overlying ice/snow. Glaciovolcanic caves (sub-horizontal) and chimneys (vertical) have been documented within a variety of volcanic regions around the world, with their formation sometimes preceding volcanic eruptions. Studying the formation and evolution of glaciovolcanic caves and chimneys and their relation to changes within the associated volcanic and glacial systems, therefore has potential to inform glaciovolcanic hazard assessments. In 2016, glaciovolcanic chimneys were discovered within Job Glacier in the Mt. Meager Volcancic Complex, British Columbia, Canada. The hypothesis that the chimneys formed as a result of glacier thinning, rather than due to an increase in volcanic activity, has yet to be tested. Here we seek to describe the morphology of these glaciovolcanic features, with respect to glaciological conditions and geothermal heat fluxes, using analytical models. By adapting existing analytical models of subglacial hydrological channels to account for the flow of geothermal gases instead of water, we derive the opening and closure rates for glaciovolcanic caves and chimneys. We use idealized glacier geometries and simplified descriptions of the energy transfer between the geothermal gases and the ice walls to facilitate our analysis. Steady-state geometries are found by balancing the melt opening, internal energy loss and the closure due to ice creep, and presented as functions of glacier thickness and geothermal heat flux. Our analytical results will be used to guide numerical simulations with more complex geometries and transient glaciovolcanic conditions. A better understanding of these complex interactions will facilitate more effective assessment of potential precursory signals of volcanic activity.