New field-verified calculation methods can provide efficient simulation tools for both pipeline design and operation analysis in assessing likely damage from dislodging a stuck pig or hydrate plug. The model derived from new methods includes calculation of all forces acting during the pig or plug dislodgement, both for and against the eventual motion. Motion begins when the pressure differential across the pig or plugs overcomes the static resistance force causing the temporary blockage. This pressure differential is the only term in the momentum balance equation moving in the same direction as the pig moves. Factors working counter to pig motion include: fluid and pig (or plug) inertia; pig and fluid friction against the pipe wall; gas expansion upstream of the pig; gas compression in front of the pig. In this work, mathematical equations provide the total mass representing inertia of the fast-moving gas and solid. The mass of the downstream compressed region and upstream expanded region is determined by the relevant gas densities. Both linear and quadratic velocity terms represent the friction between the pig and the pipe wall and Darcy's formula describes friction between gas and pipe wall in the pig adjacent compressed and expanded regions, where an average velocity has been assumed for the rarefaction wave-crossed region. It is shown, how the gas expansion upstream of the pig (or plug) decreases the available pressure differential. The downstream gas compression is derived from the linearization of a piston model. The final momentum balance equation is obtained by collecting all the above contributions, allowing a calculation of the stoppage's dynamic evolution, and predicting peak velocity during a fast start-up. The left-hand side of the equation represents the pig (and possible slug) inertia while the right-hand side shows the net force acting on the pig as a consequence of the pressure differential between trapped gas (between the kicker line and trap door) and the pressure upstream of the pig. Researchers compared the newly developed dynamic model for simulating pig or plug dislodging with available field measurements. The only published measurement value of peak velocity after sudden displacement referred to hydrate plug decomposition tests performed on a 4-in. OD gas-condensate pipeline in Wyoming. Using the current model, the hydrate plug velocity time trend after dislodging was calculated. The calculated peak velocity was 81.1 m/sec, reached after 0.6 sec. No further data are available in the open literature to test the new model with reference to pig motion. It was, however, applied to investigating an 18-in, OD lift gas pipeline incident, which occurred during pigging operations conducted as part of commissioning. The accumulation of a large amount of debris (2 tons) in front of a cleaning pig caused it to become stuck. Operators tried to displace the pig by applying a large pressure differential. The pig suddenly dislodged and caused damage in a bend close to its stuck position. Simulation of the pig displacement motion allowed estimation of its transient evolution and peak velocity. A last calculation refers to the model for the calculation of the pig arrest load on the receiving pig trap door.