A new mathematical model of aggregate of N identical spherical particles is proposed. Model is able to simulate aggregates with different flexibility. Mutual forces in normal direction between primary particles are described by spring-mass system with parameters related to the material properties. The flexibility of aggregate structure is controlled by harmonic interaction functions. Developed model was used to study the lift-off phenomenon of aggregates in the fluid. Simulation were performed for numerically generated few population of fractal-like aggregates by Diffusion Limited Aggregation algorithm (DLA), which differ with number of primary particles in aggregate’s structure and fractal dimension. Numerical results show that aggregates with more open morphology with fractal dimension in the range of Df = 1.6 - 1.8 are lifted-off easier, compared to aggregates with compacted structure. The effectiveness of the lift off is enhanced by the deformation of the aggregate caused by the flexibility of its structure.