Successfully replacing meat with plant-based options will require not only replicating the texture of muscular fibres, but also imitating the taste, aroma, and juiciness of meat as closely and realistically as possible. This study examines the impact of rapeseed oil on the textural properties of meat analogues. Pea protein and soy protein are chosen as model systems to assess the effect of rapeseed oil. Optical, mechanical, and rheological characterisation tests are conducted to investigate the oil droplet distribution, the gel strength, Young’s modulus, and the length of the LVE region. The hypothesis is that oil droplets will act as active fillers in the protein matrix, and thus, diminish the strength of the protein gel network. The results of this study show that rapeseed oil droplets act as inactive fillers, as they are not bound to both examined protein matrices. Soy protein extrudates display minimal changes, while pea protein extrudates are significantly affected by the addition of oil. For example, oil addition decreased the G′ in the LVE region of pea protein meat analogues by 50%, while soy protein samples showed no significant changes. Despite the similar interfacial activities of the investigated proteins, the decreased encapsulation efficiency of pea protein was confirmed by the higher amount of extracted oil from the respective extrudates.