An optical trap for storing femtosecond laser pulses to enhance the interaction effectiveness with optically thin targets is being proposed and investigated. Presently, we studied the trapping of 10-200 fs laser pulses of wavelength 800 nm, 1 mu J energy per pulse, and 10 Hz repetition rate. To compensate the optical losses in the trap, a Ti: Sapphire crystal as an amplifying medium is being considered, which should be synchronously pumped by the second harmonic of the Nd: YAG laser. Due to the propagation of the short pulses through optical trap components, group velocity dispersion introduces a significant broadening in pulse duration. To compensate for this broadening, a chirped mirror with suitable parameters is being proposed. An increase of the average power of the laser pulse in the optical trap that includes an amplifying medium (Ti: Sapphire crystal) by a factor of 805 compared to a single passage of the laser pulse was derived. It should be possible to store the laser pulse in the optical trap for >4 mu s with constant power and with a repetition rate of up to 250 MHz.