State-insensitive dipole trapping of multilevel atoms can be achieved by an appropriate choice of the wavelength of the trapping laser, so that the interaction with the different transitions results in equal AC Stark shifts for the ground and excited states of interest. However this approach is severely limited by the availability of coherent sources at the required wavelength and of appropriate power. This work investigates state-insensitive trapping of caesium atoms for which the required wavelength of 935.6 nm is inconvenient in terms of experimental realization. Bichromatic state-insensitive trapping is proposed to overcome the lack of suitable laser sources. We first consider pairs of laser wavelengths in the ratio 1:2 and 1:3, as obtained via second- and third- harmonic generation. We found that the wavelength combinations 931.8-1863.6 nm and 927.5-2782.5 nm are suitable for state-insensitive trapping of caesium atoms. In addition, we examine bichromatic state-insensitive trapping produced by pairs of laser wavelengths corresponding to currently available high power lasers. These wavelength pairs were found to be in the range of 585-588 nm and 623-629 for one laser and 1064-1080 nm for the other.