Volume increase between the reactants and the products of alkali silica reaction could reach up to 100%. Taking place inside the aggregates, ASR imposes internal pressure on the surrounding material. In the current paper, we study the possibility of crack growth due to such internal loading. This study is done by employing a semi-analytical mechanical model comprising an elastic solution to a well-known Eshelby problem and a linear elastic fracture mechanics solution to a ring-shaped crack encircling a spheroidal inclusion. The proposed method implies the availability of pre-existing micro-fissures within the aggregate. The study reveals dependence of the crack growing potential on the spheroid's shape: the larger is the ASR pocket - the longer crack it can open. Two most critical shapes, causing a highest stress intensity factor and developing the longest crack, are a sphere and a spheroid with 1/4 aspect ratio respectively. The size analysis of the problem suggests a critical spheroid's radius below which no crack growth is expected. For a chosen material properties and expansion value, such radius lays in the range between 0.1 and 1 micrometer. Independently of the expansion value and the shape of the pocket of ASR product, the maximum crack length has a power-law dependence on the size of a spheroid. All the theoretical predictions are confirmed by a numerical model based on the combination of the finite element method and cohesive element approach.