In this paper, a novel design method for bandpass filter with attenuation poles (BAP) is presented. The changed inverter element values due to inserting either capacitors or inductors can be optimized using the linear relationship between inverter element values of a conventional bandpass filter (BPF) and those of the BAP using the Touchstone program. A 1800-1825 MHz bandpass filter with attenuation poles for duplexers is designed and fabricated using coaxial dielectric resonators. The validity of this design approach is demonstrated by a computer simulation. The resonators are simulated equivalently as shorted lossy transmission lines. The measured results of center frequency, bandwidth, and attenuation pole frequencies closely agree with the design values.