Changes from dyke to sill propagation in the shallow crust are often caused by dissimilar layer properties. However, most previous studies have not considered the influence of glacial loading and unloading on dyke and sill deflection processes. Here, we attempt to collectively explore mechanical (layer stiffness) and geometrical (dyke dip, layer thickness) realistic parameters subject to two different magma overpressure values (namely 5 MPa and 10 MPa) that promote dyke-sill transitions in both non-glacial and glacial settings. To do this, we use as a field example, the Stardalur laccolith: a multiple stacked-sill intrusion located in SW Iceland. The laccolith lies near the retreating Langjökull glacier and was emplaced at the contact between a stiff lava layer and a soft hyaloclastite layer. We initially model two different stratigraphic crustal segments (stratigraphy a and b) and perform sensitivity analyses to investigate the likely contact opening due to the Cook-Gordon debonding and delamination mechanism under different loading conditions: magma overpressure, regional horizontal extension, glacial vertical load and a thin elastic layer at the stratigraphic contact. Our results show that contact opening (delamination) occurs in both non-glacial and glacial settings when the dissimilar mechanical contact is weak (low shear and tensile stress, zero tensile strength). In non-glacial settings, stiff layers (e.g., lavas) concentrate more tensile stress than soft layers (e.g., hyaloclastites/breccia) but accommodate less total (x–y) displacement than the surrounding host rock (e.g., soft hyaloclastites) in the vicinity of a dyke tip. Yet, a thicker hyaloclastite layer in the stratigraphy, subject to higher magma overpressure (Po = 10 MPa), may encourage dyke-sill transitions. Instead, in glacial domains, the stress conditions imposed by the variable vertical pressure of the ice cap result in higher tensile stress accumulation and displacement in stiff layers which they primarily control sill emplacement.