Magma intrusion rate is a key parameter in eruption triggering but is poorly quantified in existing geodetic studies. Here we examine two episodes of rapid inflation in this context. Two noneruptive microseismic swarms were recorded at Semisopochnoi Volcano, Alaska in 2014–2015. We use differential SAR techniques and TerraSAR‐X images to document surface deformation from 2011 to 2015, which comprises island‐wide radial inflation totaling ~25 cm (+/−1 cm) line of sight displacement in 2014–2015. Multiple source geometries are tested in an inversion of the deformation data, and InSAR data are best fit by a spheroid trending to the northeast and plunging to the southeast, with a major axis of ~4 km and minor axes of ~1 km, directly under the central caldera of Semisopochnoi. In 2014, a modeled influx of 0.043 km³ of magma caused line of sight displacement of ~17 cm. This magma was stored at a depth of ~8 km, until 2015 when 0.029 km³ was added. Along with the definition of inflation source parameters, the recorded seismic events are relocated using differential travel times. These relocated events outline a linear aseismic area within a larger zone of shallow (<10 km) seismicity. This aseismic region aligns with the centroid of the deformation model. Based on these geodetic and seismic models, the plumbing system at Semisopochnoi is interpreted as a spheroidal magma storage zone at a depth of ˜8 km below a linear feature of partial melt. The observed deformation and seismicity appear to result from rapid injection into this main storage region.