The direct relationship between early-stage breast cancer detection and survival rates has created the need for a simple, fast and cheap method to detect breast cancer at its earliest stages. Endoscopic evaluation of the mammary ducts known as ductoscopy has great potential to detect early breast cancers. Unfortunately, there are technical limitations, most notably lack of steerability and high tissue damage, limiting its practicality. A promising alternative to rigid endoscopy tools is the use of soft robots. This paper presents the computational multidomain model for the MAMMOBOT soft growing prototype. The prototype is using pressurised saline solution to achieve elongation in the breast’s ductal tree, a tendon driven catheter for steering, and an active channel for soft material storage. The derivation of the model is based on plant cell expansion, and physical modelling of the actuation and hydraulic systems. The model is validated in 1D using experimental data from the MAMMOBOT prototype. All unknown model variables were identified during a parameter investigation using Latin Hypercube Sampling. The developed hydraulic model predicted the measured elongation with a 1.7 mm RMSE error, 3.5% of the total robot length, while the combined actuation and hydraulic models predicted the elongation with 2.5 mm RMSE, 5% of total length. The results presented here is the first attempt to implement the growing robot concepts in small scales and demonstrate their accuracy. The developed model will be used to improve the closed loop control of the growing robot, improving steerability and positional accuracy, enhancing the cancer detection process.