You can use a capacitive sensor.
Use two plates positioned side by side (or opposite) as two plates of a capacitor. Use this capacitor in an oscillator ( digital oscillators will be more suitable, in some cases). The presence of metal (any metal) will increase the capacitance, lowering the frequency substantially while plastic will barely effect the frequency compared to no material present. If you know the change in capacitance (measure the frequency change), you can use a capacitor in parallel with this capacitor to keep the change with in manageable limits.
Requires placing the plates close to the object.
You need to shield against electrical and magnetic fields.
Detect oscillator frequency change using a PLL (or a monostable + D flip flop combination). You can have long lines (subjected to noise interference and magnetic / electrical fields and current drive capability of osc (+buffer)) between oscillator and PLL.
Plates could be mounted on a solid plastic sheet by bolting, assuming that you need this for some kind of objects moving on a conveyor belt.
Alternatively, you could sense change in phase of a waveform. There are more ways. Depends on your requirement and the scenario of usage. If you describe your requirement in detail and what do you want to achieve, probably a more suitable solution can be worked out.