Undue means more than is fair, reasonable, or needed. 'Undue pressure' is pressure that goes past what the situation deserves. 'Without undue delay' means without waiting any longer than the job honestly requires. 'Undue influence' is pushing someone harder than you have the right to. It goes before a noun; you do not say 'the delay was undue' in normal English. The word carries a judgement, and that is the whole reason it exists. If I say 'there was pressure', I have described a fact. If I say 'there was undue pressure', I have told you the pressure crossed a line. So it is a quiet way of complaining, or of setting a limit, without raising your voice. That is why you meet it constantly in careful, official language — contracts, law, medical advice, company rules, polite letters: 'Please do not cause the patient undue distress.' 'The company must not place undue burden on staff.' The word almost always sits with a negative noun: pressure, delay, hardship, burden, risk, influence, alarm, haste, distress. That is a useful shortcut for students. Something good is never 'undue' — you cannot say 'undue happiness'. Though actually there is a small wrinkle here that dictionaries do not always mention. Because 'undue' means 'too much', the phrase 'without undue X' does NOT mean 'without any X'. 'Without undue delay' quietly admits there will be SOME delay — just not an unreasonable amount. Officials like the phrase for exactly that reason: it promises less than it sounds like it promises.