There are many methods for computing the tsunami kinematics directly and inversely. The direct detection of waves in the deep ocean makes it possible to establish the tsunami source characteristics and origin. The present study proposes a modification in the methodology of determining tsunami travel times and wave front positions of direct and reflected waves. The initial ray approximation can be optimized with the use of an algorithm that calculates all potential variations and applies the corrections to travel time values. Such an algorithm was tested in an area with model bathymetry and compared with a non-optimized method. The modified algorithm for the calculation of travel times of reflected waves was also tested on the model bottom topography.