The presented approach for reducing the phase and group errors in short wavelength pulses propagation modeling is based upon the modal error minimization. The computational model is built of alike component substructures the matrices of which are obtained by modal synthesis. The necessary modal properties of component substructures are established by solving the total modal error minimization problem for a samplestructure the exact modal frequencies of which are known theoretically and where modal frequencies and shapes of a component substructure are used as the design parameters. After the matrices of a componentsubstructure are obtained, they can be used to form structure as higher-order elements. As a result, modelshaving 60-80% of modal frequencies with an error less than 3% can be obtained by using the optimizedcomponent substructures. Though the synthesized mass matrices are non-diagonal, the obtained dynamic modelsare able to simulate short transient waves and wave pulses propagating in elastic or acoustic environments byusing only a few nodal points per pulse length. Large computational models are subdivided into sub-domains inwhich different time and space step sizes are employed.The presented technique enables to enhance considerablythe efficiency of the simulation of acoustic-solid problems where great variations of wave propagationvelocity in different sub-domains can be observed.