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In this paper, the continuum mechanics method and a bending model is applied to obtain the resonant frequency of the fixed-free SWCNT where the mass is rigidly attached to the tip. This method used the Euler–Bernoulli theory with cantilevered boundary conditions where the effect of attached mass on resonant frequency, is added at the free end condition. The resonant frequencies of the fixed-free SWCNT have been investigated. The results showed the sensitivity of the single walled carbon nanotubes to different masses. Moreover, they indicate that by increasing the value of attached mass, the values of resonant frequency are decreased. The validity and the accuracy of these formulas are examined with other sensor equations in the literatures. The results indicate that the new sensor equations can be used for CNT like CNT-based biosensors with reasonable accuracy.